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#cython: language_level=3
#cython: boundscheck=False
#cython: wraparound=False
#cython: cdivision=True
"""
cython_profiles.pyx
cython implementation of the isi-, spike- and spike-sync profiles
Note: using cython memoryviews (e.g. double[:]) instead of ndarray objects
improves the performance of spike_distance by a factor of 10!
Copyright 2014-2015, Mario Mulansky <mario.mulansky@gmx.net>
Distributed under the BSD License
"""
"""
To test whether things can be optimized: remove all yellow stuff
in the html output::
cython -a cython_profiles.pyx
which gives::
cython_profiles.html
"""
import numpy as np
cimport numpy as np
from libc.math cimport fabs
from libc.math cimport fmax
from libc.math cimport fmin
from pyspike.cython.cython_get_tau cimport get_tau
#DTYPE = float
#ctypedef np.float_t DTYPE_t
############################################################
# isi_profile_cython
############################################################
def isi_profile_cython(double[:] s1, double[:] s2,
double t_start, double t_end,
double MRTS=0.):
cdef double[:] spike_events
cdef double[:] isi_values
cdef int index1, index2, index
cdef int N1, N2
cdef double nu1, nu2
N1 = len(s1)
N2 = len(s2)
spike_events = np.empty(N1+N2+2)
# the values have one entry less as they are defined at the intervals
isi_values = np.empty(N1+N2+1)
# first x-value of the profile
spike_events[0] = t_start
# first interspike interval - check if a spike exists at the start time
if s1[0] > t_start:
# edge correction
nu1 = fmax(s1[0]-t_start, s1[1]-s1[0]) if N1 > 1 else s1[0]-t_start
index1 = -1
else:
nu1 = s1[1]-s1[0] if N1 > 1 else t_end-s1[0]
index1 = 0
if s2[0] > t_start:
# edge correction
nu2 = fmax(s2[0]-t_start, s2[1]-s2[0]) if N2 > 1 else s2[0]-t_start
index2 = -1
else:
nu2 = s2[1]-s2[0] if N2 > 1 else t_end-s2[0]
index2 = 0
isi_values[0] = fabs(nu1-nu2)/fmax(MRTS, fmax(nu1, nu2))
index = 1
with nogil: # release the interpreter to allow multithreading
while index1+index2 < N1+N2-2:
# check which spike is next, only if there are spikes left in 1
# next spike in 1 is earlier, or there are no spikes left in 2
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 = fmax(t_end-s1[index1], nu1) if N1 > 1 \
else t_end-s1[index1]
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 = fmax(t_end-s2[index2], nu2) if N2 > 1 \
else t_end-s2[index2]
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 = fmax(t_end-s1[index1], nu1) if N1 > 1 \
else t_end-s1[index1]
if index2 < N2-1:
nu2 = s2[index2+1]-s2[index2]
else:
# edge correction
nu2 = fmax(t_end-s2[index2], nu2) if N2 > 1 \
else t_end-s2[index2]
# compute the corresponding isi-distance
isi_values[index] = fabs(nu1 - nu2) / fmax(MRTS, fmax(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
# end nogil
return spike_events[:index+1], isi_values[:index]
############################################################
# get_min_dist_cython
############################################################
cdef inline double get_min_dist_cython(double spike_time,
double[:] spike_train,
# use memory view to ensure inlining
# np.ndarray[DTYPE_t,ndim=1] spike_train,
int N,
int start_index,
double t_start, double t_end) nogil:
""" Returns the minimal distance |spike_time - spike_train[i]|
with i>=start_index.
"""
cdef double d, d_temp
# start with the distance to the start time
d = fabs(spike_time - t_start)
if start_index < 0:
start_index = 0
while start_index < N:
d_temp = fabs(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 = fabs(t_end - spike_time)
if d_temp > d:
return d
else:
return d_temp
############################################################
# dist_at_t
############################################################
cdef inline double dist_at_t(double isi1, double isi2,
double s1, double s2,
double MRTS, int RI) nogil:
""" Compute instantaneous Spike Distance
In: isi1, isi2 - spike time differences around current times in each trains
s1, s2 - weighted spike time differences between trains
MRTS -minimum relevant time scal (0 for legacy logic)
RI - Rate Independent Adaptive spike distance
(False for legacy SPIKE distance)
Out: Spike Distance at current time
"""
cdef double meanISI = .5*(isi1+isi2)
cdef double limitedISI = max(MRTS, meanISI)
if RI:
return .5*(s1+s2)/limitedISI
else:
return .5*(s1*isi2 + s2*isi1)/(meanISI*limitedISI)
############################################################
# spike_profile_cython
############################################################
def spike_profile_cython(double[:] t1, double[:] t2,
double t_start, double t_end,
double MRTS=0., int RI=0):
cdef double[:] spike_events
cdef double[:] y_starts
cdef double[:] y_ends
cdef double[:] t_aux1 = np.empty(2)
cdef double[:] t_aux2 = np.empty(2)
cdef int N1, N2, index1, index2, index
cdef double t_p1, t_f1, t_p2, t_f2, dt_p1, dt_p2, dt_f1, dt_f2
cdef double isi1, isi2, s1, s2
N1 = len(t1)
N2 = len(t2)
# we can assume at least one spikes per spike train
assert N1 > 0
assert N2 > 0
spike_events = np.empty(N1+N2+2)
y_starts = np.empty(len(spike_events)-1)
y_ends = np.empty(len(spike_events)-1)
with nogil: # release the interpreter to allow multithreading
spike_events[0] = t_start
# t_p1 = t_start
# t_p2 = t_start
# auxiliary spikes for edge correction - consistent with first/last ISI
t_aux1[0] = fmin(t_start, 2*t1[0]-t1[1]) if N1 > 1 else t_start
t_aux1[1] = fmax(t_end, 2*t1[N1-1]-t1[N1-2]) if N1 > 1 else t_end
t_aux2[0] = fmin(t_start, 2*t2[0]-t2[1]) if N2 > 1 else t_start
t_aux2[1] = fmax(t_end, 2*t2[N2-1]-t2[N2-2]) if N2 > 1 else t_end
t_p1 = t_start if (t1[0] == t_start) else t_aux1[0]
t_p2 = t_start if (t2[0] == t_start) else t_aux2[0]
if t1[0] > t_start:
# dt_p1 = t2[0]-t_start
t_f1 = t1[0]
dt_f1 = get_min_dist_cython(t_f1, t2, N2, 0, t_aux2[0], t_aux2[1])
isi1 = fmax(t_f1-t_start, t1[1]-t1[0]) if N1 > 1 else t_f1-t_start
dt_p1 = dt_f1
# s1 = dt_p1*(t_f1-t_start)/isi1
s1 = dt_p1
index1 = -1
else:
t_f1 = t1[1] if N1 > 1 else t_end
dt_f1 = get_min_dist_cython(t_f1, t2, N2, 0, t_aux2[0], t_aux2[1])
dt_p1 = get_min_dist_cython(t_p1, t2, N2, 0, t_aux2[0], t_aux2[1])
isi1 = t_f1-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_cython(t_f2, t1, N1, 0, t_aux1[0], t_aux1[1])
dt_p2 = dt_f2
isi2 = fmax(t_f2-t_start, t2[1]-t2[0]) if N2 > 1 else t_f2-t_start
# s2 = dt_p2*(t_f2-t_start)/isi2
s2 = dt_p2
index2 = -1
else:
t_f2 = t2[1] if N2 > 1 else t_end
dt_f2 = get_min_dist_cython(t_f2, t1, N1, 0, t_aux1[0], t_aux1[1])
dt_p2 = get_min_dist_cython(t_p2, t1, N1, 0, t_aux1[0], t_aux1[1])
isi2 = t_f2-t2[0]
s2 = dt_p2
index2 = 0
y_starts[0] = dist_at_t(isi1, isi2, s1, s2, MRTS, RI)
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_aux1[1]
spike_events[index] = t_p1
s2 = (dt_p2*(t_f2-t_p1) + dt_f2*(t_p1-t_p2)) / isi2
y_ends[index-1] = dist_at_t(isi1, isi2, s1, s2, MRTS, RI)
# now the next interval start value
if index1 < N1-1:
dt_f1 = get_min_dist_cython(t_f1, t2, N2, index2,
t_aux2[0], t_aux2[1])
isi1 = t_f1-t_p1
s1 = dt_p1
else:
dt_f1 = dt_p1
isi1 = fmax(t_end-t1[N1-1], t1[N1-1]-t1[N1-2]) if N1 > 1 \
else t_end-t1[N1-1]
# s1 needs adjustment due to change of isi1
# s1 = dt_p1*(t_end-t1[N1-1])/isi1
# Eero's correction: no adjustment
s1 = dt_p1
# s2 is the same as above, thus we can compute y2 immediately
y_starts[index] = dist_at_t(isi1, isi2, s1, s2, MRTS, RI)
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_p2 contains the current time point
# get the next time
if index2 < N2-1:
t_f2 = t2[index2+1]
else:
t_f2 = t_aux2[1]
spike_events[index] = t_p2
s1 = (dt_p1*(t_f1-t_p2) + dt_f1*(t_p2-t_p1)) / isi1
y_ends[index-1] = dist_at_t(isi1, isi2, s1, s2, MRTS, RI)
# now the next interval start value
if index2 < N2-1:
dt_f2 = get_min_dist_cython(t_f2, t1, N1, index1,
t_aux1[0], t_aux1[1])
isi2 = t_f2-t_p2
s2 = dt_p2
else:
dt_f2 = dt_p2
isi2 = fmax(t_end-t2[N2-1], t2[N2-1]-t2[N2-2]) if N2 > 1 \
else t_end-t2[N2-1]
# s2 needs adjustment due to change of isi2
# s2 = dt_p2*(t_end-t2[N2-1])/isi2
# Eero's correction: no adjustment
s2 = dt_p2
# s2 is the same as above, thus we can compute y2 immediately
y_starts[index] = dist_at_t(isi1, isi2, s1, s2, MRTS, RI)
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_cython(t_f1, t2, N2, index2,
t_aux2[0], t_aux2[1])
isi1 = t_f1 - t_p1
else:
t_f1 = t_aux1[1]
dt_f1 = dt_p1
isi1 = fmax(t_end-t1[N1-1], t1[N1-1]-t1[N1-2]) if N1 > 1 \
else t_end-t1[N1-1]
if index2 < N2-1:
t_f2 = t2[index2+1]
dt_f2 = get_min_dist_cython(t_f2, t1, N1, index1,
t_aux1[0], t_aux1[1])
isi2 = t_f2 - t_p2
else:
t_f2 = t_aux2[1]
dt_f2 = dt_p2
isi2 = fmax(t_end-t2[N2-1], t2[N2-1]-t2[N2-2]) if N2 > 1 \
else t_end-t2[N2-1]
index += 1
# the last event is the interval end
if spike_events[index-1] == t_end:
index -= 1
else:
spike_events[index] = t_end
s1 = dt_f1
s2 = dt_f2
y_ends[index-1] = dist_at_t(isi1, isi2, s1, s2, MRTS, RI)
# end nogil
# 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]
############################################################
# coincidence_profile_cython
############################################################
def coincidence_profile_cython(double[:] spikes1, double[:] spikes2,
double t_start, double t_end, double max_tau, double MRTS=0):
cdef int N1 = len(spikes1)
cdef int N2 = len(spikes2)
cdef int i = -1
cdef int j = -1
cdef int n = 0
cdef double[:] st = np.zeros(N1 + N2 + 2) # spike times
cdef double[:] c = np.zeros(N1 + N2 + 2) # coincidences
cdef double[:] mp = np.ones(N1 + N2 + 2) # multiplicity
cdef double interval = t_end - t_start
cdef double tau
cdef double true_max = t_end - t_start
if max_tau > 0:
true_max = fmin(true_max, 2*max_tau)
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, true_max, MRTS)
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, true_max, MRTS)
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
############################################################
# coincidence_single_profile_cython
############################################################
def coincidence_single_profile_cython(double[:] spikes1, double[:] spikes2,
double t_start, double t_end, double max_tau, double MRTS=0.):
cdef int N1 = len(spikes1)
cdef int N2 = len(spikes2)
cdef int j = -1
cdef double[:] c = np.zeros(N1) # coincidences
cdef double interval = t_end - t_start
cdef double tau
cdef double true_max = t_end - t_start
if max_tau > 0:
true_max = fmin(true_max, 2*max_tau)
for i in xrange(N1):
while j < N2-1 and spikes2[j+1] < spikes1[i]:
# move forward until spikes2[j] is the last spike before spikes1[i]
# note that if spikes2[j] is after spikes1[i] we dont do anything
j += 1
tau = get_tau(spikes1, spikes2, i, j, true_max, MRTS)
if j > -1 and fabs(spikes1[i]-spikes2[j]) < tau:
# current spike in st1 is coincident
c[i] = 1
if j < N2-1 and (j < 0 or spikes2[j] < spikes1[i]):
# in case spikes2[j] is before spikes1[i] it has to be the one
# right before (see above), hence we move one forward and also
# check the next spike
j += 1
tau = get_tau(spikes1, spikes2, i, j, true_max, MRTS)
if fabs(spikes2[j]-spikes1[i]) < tau:
# current spike in st1 is coincident
c[i] = 1
return c
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