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# Module containing functions to compute the SPIKE directionality and the
# spike train order profile
# Copyright 2015, Mario Mulansky <mario.mulansky@gmx.net>
# Distributed under the BSD License
import numpy as np
from math import exp
import pyspike
from pyspike import DiscreteFunc
############################################################
# spike_directionality
############################################################
def spike_directionality(spike_train1, spike_train2, normalize=True,
interval=None, max_tau=None):
""" Computes the overall spike directionality 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_directionality_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_directionality_matrix
############################################################
def spike_directionality_matrix(spike_trains, normalize=True, indices=None,
interval=None, max_tau=None):
""" Computes the spike directionaity 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_directionality(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_train_order_profile
############################################################
def spike_train_order_profile(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_spike_train_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_directionality_matrix(spike_trains, normalize=False,
indices=indices, interval=interval,
max_tau=max_tau)
return optimal_spike_train_order_from_matrix(D, full_output)
############################################################
# permutate_matrix
############################################################
def permutate_matrix(D, p):
""" Applies the permutation p to the columns and rows of matrix D.
Return the new permutated matrix.
"""
N = len(D)
D_p = np.empty_like(D)
for n in xrange(N):
for m in xrange(N):
D_p[n, m] = D[p[n], p[m]]
return D_p
# internal helper functions
############################################################
# _spike_directionality_profile
############################################################
def _spike_directionality_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)
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