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""" python_backend.py
Collection of python functions that can be used instead of the cython
implementation.
Copyright 2014, Mario Mulansky <mario.mulansky@gmx.net>
Distributed under the BSD License
"""
import numpy as np
############################################################
# isi_distance_python
############################################################
def isi_distance_python(s1, s2, t_start, t_end):
""" Plain Python implementation of the isi distance.
"""
N1 = len(s1)
N2 = len(s2)
# compute the isi-distance
spike_events = np.empty(N1+N2+2)
spike_events[0] = t_start
# the values have one entry less - the number of intervals between events
isi_values = np.empty(len(spike_events) - 1)
if s1[0] > t_start:
# edge correction
nu1 = max(s1[0] - t_start, s1[1] - s1[0])
index1 = -1
else:
nu1 = s1[1] - s1[0]
index1 = 0
if s2[0] > t_start:
# edge correction
nu2 = max(s2[0] - t_start, s2[1] - s2[0])
index2 = -1
else:
nu2 = s2[1] - s2[0]
index2 = 0
isi_values[0] = abs(nu1 - nu2) / max(nu1, nu2)
index = 1
while index1+index2 < N1+N2-2:
# check which spike is next - from s1 or s2
if (index1 < N1-1) and (index2 == N2-1 or s1[index1+1] < s2[index2+1]):
index1 += 1
spike_events[index] = s1[index1]
if index1 < N1-1:
nu1 = s1[index1+1]-s1[index1]
else:
# edge correction
nu1 = max(t_end-s1[N1-1], s1[N1-1]-s1[N1-2])
elif (index2 < N2-1) and (index1 == N1-1 or
s1[index1+1] > s2[index2+1]):
index2 += 1
spike_events[index] = s2[index2]
if index2 < N2-1:
nu2 = s2[index2+1]-s2[index2]
else:
# edge correction
nu2 = max(t_end-s2[N2-1], s2[N2-1]-s2[N2-2])
else: # s1[index1 + 1] == s2[index2 + 1]
index1 += 1
index2 += 1
spike_events[index] = s1[index1]
if index1 < N1-1:
nu1 = s1[index1+1]-s1[index1]
else:
# edge correction
nu1 = max(t_end-s1[N1-1], s1[N1-1]-s1[N1-2])
if index2 < N2-1:
nu2 = s2[index2+1]-s2[index2]
else:
# edge correction
nu2 = max(t_end-s2[N2-1], s2[N2-1]-s2[N2-2])
# compute the corresponding isi-distance
isi_values[index] = abs(nu1 - nu2) / \
max(nu1, nu2)
index += 1
# the last event is the interval end
if spike_events[index-1] == t_end:
index -= 1
else:
spike_events[index] = t_end
# use only the data added above
# could be less than original length due to equal spike times
return spike_events[:index + 1], isi_values[:index]
############################################################
# get_min_dist
############################################################
def get_min_dist(spike_time, spike_train, start_index, t_start, t_end):
""" Returns the minimal distance |spike_time - spike_train[i]|
with i>=start_index.
"""
d = abs(spike_time - t_start)
if start_index < 0:
start_index = 0
while start_index < len(spike_train):
d_temp = abs(spike_time - spike_train[start_index])
if d_temp > d:
return d
else:
d = d_temp
start_index += 1
# finally, check the distance to end time
d_temp = abs(t_end - spike_time)
if d_temp > d:
return d
else:
return d_temp
############################################################
# spike_distance_python
############################################################
def spike_distance_python(spikes1, spikes2, t_start, t_end):
""" Computes the instantaneous spike-distance S_spike (t) of the two given
spike trains. 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.
- t_start, t_end: edges of the spike train
Returns:
- PieceWiseLinFunc describing the spike-distance.
"""
# shorter variables
t1 = spikes1
t2 = spikes2
N1 = len(t1)
N2 = len(t2)
spike_events = np.empty(N1+N2+2)
y_starts = np.empty(len(spike_events)-1)
y_ends = np.empty(len(spike_events)-1)
spike_events[0] = t_start
t_p1 = t_start
t_p2 = t_start
if t1[0] > t_start:
t_f1 = t1[0]
dt_f1 = get_min_dist(t_f1, t2, 0, t_start, t_end)
dt_p1 = dt_f1
isi1 = max(t_f1-t_start, t1[1]-t1[0])
s1 = dt_p1*(t_f1-t_start)/isi1
index1 = -1
else:
dt_p1 = 0.0
t_f1 = t1[1]
dt_f1 = get_min_dist(t_f1, t2, 0, t_start, t_end)
isi1 = t1[1]-t1[0]
s1 = dt_p1
index1 = 0
if t2[0] > t_start:
# dt_p1 = t2[0]-t_start
t_f2 = t2[0]
dt_f2 = get_min_dist(t_f2, t1, 0, t_start, t_end)
dt_p2 = dt_f2
isi2 = max(t_f2-t_start, t2[1]-t2[0])
s2 = dt_p2*(t_f2-t_start)/isi2
index2 = -1
else:
dt_p2 = 0.0
t_f2 = t2[1]
dt_f2 = get_min_dist(t_f2, t1, 0, t_start, t_end)
isi2 = t2[1]-t2[0]
s2 = dt_p2
index2 = 0
y_starts[0] = (s1*isi2 + s2*isi1) / (0.5*(isi1+isi2)**2)
index = 1
while index1+index2 < N1+N2-2:
# print(index, index1, index2)
if (index1 < N1-1) and (t_f1 < t_f2 or index2 == N2-1):
index1 += 1
# first calculate the previous interval end value
s1 = dt_f1*(t_f1-t_p1) / isi1
# the previous time now was the following time before:
dt_p1 = dt_f1
t_p1 = t_f1 # t_p1 contains the current time point
# get the next time
if index1 < N1-1:
t_f1 = t1[index1+1]
else:
t_f1 = t_end
spike_events[index] = t_p1
s2 = (dt_p2*(t_f2-t_p1) + dt_f2*(t_p1-t_p2)) / isi2
y_ends[index-1] = (s1*isi2 + s2*isi1) / (0.5*(isi1+isi2)**2)
# now the next interval start value
if index1 < N1-1:
dt_f1 = get_min_dist(t_f1, t2, index2, t_start, t_end)
isi1 = t_f1-t_p1
s1 = dt_p1
else:
dt_f1 = dt_p1
isi1 = max(t_end-t1[N1-1], t1[N1-1]-t1[N1-2])
# s1 needs adjustment due to change of isi1
s1 = dt_p1*(t_end-t1[N1-1])/isi1
# s2 is the same as above, thus we can compute y2 immediately
y_starts[index] = (s1*isi2 + s2*isi1) / (0.5*(isi1+isi2)**2)
elif (index2 < N2-1) and (t_f1 > t_f2 or index1 == N1-1):
index2 += 1
# first calculate the previous interval end value
s2 = dt_f2*(t_f2-t_p2) / isi2
# the previous time now was the following time before:
dt_p2 = dt_f2
t_p2 = t_f2 # t_p1 contains the current time point
# get the next time
if index2 < N2-1:
t_f2 = t2[index2+1]
else:
t_f2 = t_end
spike_events[index] = t_p2
s1 = (dt_p1*(t_f1-t_p2) + dt_f1*(t_p2-t_p1)) / isi1
y_ends[index-1] = (s1*isi2 + s2*isi1) / (0.5*(isi1+isi2)**2)
# now the next interval start value
if index2 < N2-1:
dt_f2 = get_min_dist(t_f2, t1, index1, t_start, t_end)
isi2 = t_f2-t_p2
s2 = dt_p2
else:
dt_f2 = dt_p2
isi2 = max(t_end-t2[N2-1], t2[N2-1]-t2[N2-2])
# s2 needs adjustment due to change of isi2
s2 = dt_p2*(t_end-t2[N2-1])/isi2
# s2 is the same as above, thus we can compute y2 immediately
y_starts[index] = (s1*isi2 + s2*isi1) / (0.5*(isi1+isi2)**2)
else: # t_f1 == t_f2 - generate only one event
index1 += 1
index2 += 1
t_p1 = t_f1
t_p2 = t_f2
dt_p1 = 0.0
dt_p2 = 0.0
spike_events[index] = t_f1
y_ends[index-1] = 0.0
y_starts[index] = 0.0
if index1 < N1-1:
t_f1 = t1[index1+1]
dt_f1 = get_min_dist(t_f1, t2, index2, t_start, t_end)
isi1 = t_f1 - t_p1
else:
t_f1 = t_end
dt_f1 = dt_p1
isi1 = max(t_end-t1[N1-1], t1[N1-1]-t1[N1-2])
if index2 < N2-1:
t_f2 = t2[index2+1]
dt_f2 = get_min_dist(t_f2, t1, index1, t_start, t_end)
isi2 = t_f2 - t_p2
else:
t_f2 = t_end
dt_f2 = dt_p2
isi2 = max(t_end-t2[N2-1], t2[N2-1]-t2[N2-2])
index += 1
# the last event is the interval end
if spike_events[index-1] == t_end:
index -= 1
else:
spike_events[index] = t_end
# the ending value of the last interval
isi1 = max(t_end-t1[N1-1], t1[N1-1]-t1[N1-2])
isi2 = max(t_end-t2[N2-1], t2[N2-1]-t2[N2-2])
s1 = dt_f1*(t_end-t1[N1-1])/isi1
s2 = dt_f2*(t_end-t2[N2-1])/isi2
y_ends[index-1] = (s1*isi2 + s2*isi1) / (0.5*(isi1+isi2)**2)
# use only the data added above
# could be less than original length due to equal spike times
return spike_events[:index+1], y_starts[:index], y_ends[:index]
############################################################
# cumulative_sync_python
############################################################
def cumulative_sync_python(spikes1, spikes2):
def get_tau(spikes1, spikes2, i, j):
return 0.5*min([spikes1[i]-spikes1[i-1], spikes1[i+1]-spikes1[i],
spikes2[j]-spikes2[j-1], spikes2[j+1]-spikes2[j]])
N1 = len(spikes1)
N2 = len(spikes2)
i = 0
j = 0
n = 0
st = np.zeros(N1 + N2 - 2)
c = np.zeros(N1 + N2 - 3)
c[0] = 0
st[0] = 0
while n < N1 + N2:
if spikes1[i+1] < spikes2[j+1]:
i += 1
n += 1
tau = get_tau(spikes1, spikes2, i, j)
st[n] = spikes1[i]
if spikes1[i]-spikes2[j] > tau:
c[n] = c[n-1]
else:
c[n] = c[n-1]+1
elif spikes1[i+1] > spikes2[j+1]:
j += 1
n += 1
tau = get_tau(spikes1, spikes2, i, j)
st[n] = spikes2[j]
if spikes2[j]-spikes1[i] > tau:
c[n] = c[n-1]
else:
c[n] = c[n-1]+1
else: # spikes1[i+1] = spikes2[j+1]
j += 1
i += 1
if i == N1-1 or j == N2-1:
break
n += 1
st[n] = spikes1[i]
c[n] = c[n-1]
n += 1
st[n] = spikes1[i]
c[n] = c[n-1]+1
c[0] = 0
st[0] = spikes1[0]
st[-1] = spikes1[-1]
return st, c
############################################################
# coincidence_python
############################################################
def coincidence_python(spikes1, spikes2, t_start, t_end, max_tau):
def get_tau(spikes1, spikes2, i, j, max_tau):
m = t_end - t_start # use interval as initial tau
if i < len(spikes1)-1 and i > -1:
m = min(m, spikes1[i+1]-spikes1[i])
if j < len(spikes2)-1 and j > -1:
m = min(m, spikes2[j+1]-spikes2[j])
if i > 0:
m = min(m, spikes1[i]-spikes1[i-1])
if j > 0:
m = min(m, spikes2[j]-spikes2[j-1])
m *= 0.5
if max_tau > 0.0:
m = min(m, max_tau)
return m
N1 = len(spikes1)
N2 = len(spikes2)
i = -1
j = -1
n = 0
st = np.zeros(N1 + N2 + 2) # spike times
c = np.zeros(N1 + N2 + 2) # coincidences
mp = np.ones(N1 + N2 + 2) # multiplicity
while i + j < N1 + N2 - 2:
if (i < N1-1) and (j == N2-1 or spikes1[i+1] < spikes2[j+1]):
i += 1
n += 1
tau = get_tau(spikes1, spikes2, i, j, max_tau)
st[n] = spikes1[i]
if j > -1 and spikes1[i]-spikes2[j] < tau:
# coincidence between the current spike and the previous spike
# both get marked with 1
c[n] = 1
c[n-1] = 1
elif (j < N2-1) and (i == N1-1 or spikes1[i+1] > spikes2[j+1]):
j += 1
n += 1
tau = get_tau(spikes1, spikes2, i, j, max_tau)
st[n] = spikes2[j]
if i > -1 and spikes2[j]-spikes1[i] < tau:
# coincidence between the current spike and the previous spike
# both get marked with 1
c[n] = 1
c[n-1] = 1
else: # spikes1[i+1] = spikes2[j+1]
# advance in both spike trains
j += 1
i += 1
n += 1
# add only one event, but with coincidence 2 and multiplicity 2
st[n] = spikes1[i]
c[n] = 2
mp[n] = 2
st = st[:n+2]
c = c[:n+2]
mp = mp[:n+2]
st[0] = t_start
st[len(st)-1] = t_end
if N1 + N2 > 0:
c[0] = c[1]
c[len(c)-1] = c[len(c)-2]
mp[0] = mp[1]
mp[len(mp)-1] = mp[len(mp)-2]
else:
c[0] = 1
c[1] = 1
return st, c, mp
############################################################
# add_piece_wise_const_python
############################################################
def add_piece_wise_const_python(x1, y1, x2, y2):
x_new = np.empty(len(x1) + len(x2))
y_new = np.empty(len(x_new)-1)
x_new[0] = x1[0]
y_new[0] = y1[0] + y2[0]
index1 = 0
index2 = 0
index = 0
while (index1+1 < len(y1)) and (index2+1 < len(y2)):
index += 1
# print(index1+1, x1[index1+1], y1[index1+1], x_new[index])
if x1[index1+1] < x2[index2+1]:
index1 += 1
x_new[index] = x1[index1]
elif x1[index1+1] > x2[index2+1]:
index2 += 1
x_new[index] = x2[index2]
else: # x1[index1+1] == x2[index2+1]:
index1 += 1
index2 += 1
x_new[index] = x1[index1]
y_new[index] = y1[index1] + y2[index2]
# one array reached the end -> copy the contents of the other to the end
if index1+1 < len(y1):
x_new[index+1:index+1+len(x1)-index1-1] = x1[index1+1:]
y_new[index+1:index+1+len(y1)-index1-1] = y1[index1+1:] + y2[-1]
index += len(x1)-index1-2
elif index2+1 < len(y2):
x_new[index+1:index+1+len(x2)-index2-1] = x2[index2+1:]
y_new[index+1:index+1+len(y2)-index2-1] = y2[index2+1:] + y1[-1]
index += len(x2)-index2-2
else: # both arrays reached the end simultaneously
# only the last x-value missing
x_new[index+1] = x1[-1]
# the last value is again the end of the interval
# x_new[index+1] = x1[-1]
# only use the data that was actually filled
return x_new[:index+2], y_new[:index+1]
############################################################
# add_piece_lin_const_python
############################################################
def add_piece_wise_lin_python(x1, y11, y12, x2, y21, y22):
x_new = np.empty(len(x1) + len(x2))
y1_new = np.empty(len(x_new)-1)
y2_new = np.empty_like(y1_new)
x_new[0] = x1[0]
y1_new[0] = y11[0] + y21[0]
index1 = 0 # index for self
index2 = 0 # index for f
index = 0 # index for new
while (index1+1 < len(y11)) and (index2+1 < len(y21)):
# print(index1+1, x1[index1+1], self.y[index1+1], x_new[index])
if x1[index1+1] < x2[index2+1]:
# first compute the end value of the previous interval
# linear interpolation of the interval
y = y21[index2] + (y22[index2]-y21[index2]) * \
(x1[index1+1]-x2[index2]) / (x2[index2+1]-x2[index2])
y2_new[index] = y12[index1] + y
index1 += 1
index += 1
x_new[index] = x1[index1]
# and the starting value for the next interval
y1_new[index] = y11[index1] + y
elif x1[index1+1] > x2[index2+1]:
# first compute the end value of the previous interval
# linear interpolation of the interval
y = y11[index1] + (y12[index1]-y11[index1]) * \
(x2[index2+1]-x1[index1]) / \
(x1[index1+1]-x1[index1])
y2_new[index] = y22[index2] + y
index2 += 1
index += 1
x_new[index] = x2[index2]
# and the starting value for the next interval
y1_new[index] = y21[index2] + y
else: # x1[index1+1] == x2[index2+1]:
y2_new[index] = y12[index1] + y22[index2]
index1 += 1
index2 += 1
index += 1
x_new[index] = x1[index1]
y1_new[index] = y11[index1] + y21[index2]
# one array reached the end -> copy the contents of the other to the end
if index1+1 < len(y11):
# compute the linear interpolations values
y = y21[index2] + (y22[index2]-y21[index2]) * \
(x1[index1+1:-1]-x2[index2]) / (x2[index2+1]-x2[index2])
x_new[index+1:index+1+len(x1)-index1-1] = x1[index1+1:]
y1_new[index+1:index+1+len(y11)-index1-1] = y11[index1+1:]+y
y2_new[index:index+len(y12)-index1-1] = y12[index1:-1] + y
index += len(x1)-index1-2
elif index2+1 < len(y21):
# compute the linear interpolations values
y = y11[index1] + (y12[index1]-y11[index1]) * \
(x2[index2+1:-1]-x1[index1]) / \
(x1[index1+1]-x1[index1])
x_new[index+1:index+1+len(x2)-index2-1] = x2[index2+1:]
y1_new[index+1:index+1+len(y21)-index2-1] = y21[index2+1:] + y
y2_new[index:index+len(y22)-index2-1] = y22[index2:-1] + y
index += len(x2)-index2-2
else: # both arrays reached the end simultaneously
# only the last x-value missing
x_new[index+1] = x1[-1]
# finally, the end value for the last interval
y2_new[index] = y12[-1]+y22[-1]
# only use the data that was actually filled
return x_new[:index+2], y1_new[:index+1], y2_new[:index+1]
############################################################
# add_discrete_function_python
############################################################
def add_discrete_function_python(x1, y1, mp1, x2, y2, mp2):
x_new = np.empty(len(x1) + len(x2))
y_new = np.empty_like(x_new)
mp_new = np.empty_like(x_new)
x_new[0] = x1[0]
index1 = 0
index2 = 0
index = 0
while (index1+1 < len(y1)) and (index2+1 < len(y2)):
if x1[index1+1] < x2[index2+1]:
index1 += 1
index += 1
x_new[index] = x1[index1]
y_new[index] = y1[index1]
mp_new[index] = mp1[index1]
elif x1[index1+1] > x2[index2+1]:
index2 += 1
index += 1
x_new[index] = x2[index2]
y_new[index] = y2[index2]
mp_new[index] = mp2[index2]
else: # x1[index1+1] == x2[index2+1]
index1 += 1
index2 += 1
index += 1
x_new[index] = x1[index1]
y_new[index] = y1[index1] + y2[index2]
mp_new[index] = mp1[index1] + mp2[index2]
# one array reached the end -> copy the contents of the other to the end
if index1+1 < len(y1):
x_new[index+1:index+1+len(x1)-index1-1] = x1[index1+1:]
y_new[index+1:index+1+len(x1)-index1-1] = y1[index1+1:]
mp_new[index+1:index+1+len(x1)-index1-1] = mp1[index1+1:]
index += len(x1)-index1-1
elif index2+1 < len(y2):
x_new[index+1:index+1+len(x2)-index2-1] = x2[index2+1:]
y_new[index+1:index+1+len(x2)-index2-1] = y2[index2+1:]
mp_new[index+1:index+1+len(x2)-index2-1] = mp2[index2+1:]
index += len(x2)-index2-1
# else: # both arrays reached the end simultaneously
# x_new[index+1] = x1[-1]
# y_new[index+1] = y1[-1] + y2[-1]
# mp_new[index+1] = mp1[-1] + mp2[-1]
y_new[0] = y_new[1]
mp_new[0] = mp_new[1]
# the last value is again the end of the interval
# only use the data that was actually filled
return x_new[:index+1], y_new[:index+1], mp_new[:index+1]
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