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#cython: boundscheck=False
#cython: wraparound=False
#cython: cdivision=True
"""
cython_distances.pyx
cython implementation of the isi- and spike-distance
Note: using cython memoryviews (e.g. double[:]) instead of ndarray objects
improves the performance of spike_distance by a factor of 10!
Copyright 2014, 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_distance.pyx
which gives::
cython_distance.html
"""
import numpy as np
cimport numpy as np
from libc.math cimport fabs
from libc.math cimport fmax
from libc.math cimport fmin
DTYPE = np.float
ctypedef np.float_t DTYPE_t
############################################################
# isi_distance_cython
############################################################
def isi_distance_cython(double[:] s1,
double[:] s2):
cdef double[:] spike_events
cdef double[:] isi_values
cdef int index1, index2, index
cdef int N1, N2
cdef double nu1, nu2
N1 = len(s1)-1
N2 = len(s2)-1
nu1 = s1[1]-s1[0]
nu2 = s2[1]-s2[0]
spike_events = np.empty(N1+N2)
spike_events[0] = s1[0]
# the values have one entry less - the number of intervals between events
isi_values = np.empty(N1+N2-1)
with nogil: # release the interpreter to allow multithreading
isi_values[0] = fabs(nu1-nu2)/fmax(nu1, nu2)
index1 = 0
index2 = 0
index = 1
while True:
# check which spike is next - from s1 or s2
if s1[index1+1] < s2[index2+1]:
index1 += 1
# break condition relies on existence of spikes at T_end
if index1 >= N1:
break
spike_events[index] = s1[index1]
nu1 = s1[index1+1]-s1[index1]
elif s1[index1+1] > s2[index2+1]:
index2 += 1
if index2 >= N2:
break
spike_events[index] = s2[index2]
nu2 = s2[index2+1]-s2[index2]
else: # s1[index1+1] == s2[index2+1]
index1 += 1
index2 += 1
if (index1 >= N1) or (index2 >= N2):
break
spike_events[index] = s1[index1]
nu1 = s1[index1+1]-s1[index1]
nu2 = s2[index2+1]-s2[index2]
# compute the corresponding isi-distance
isi_values[index] = fabs(nu1 - nu2) / fmax(nu1, nu2)
index += 1
# the last event is the interval end
spike_events[index] = s1[N1]
# 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=0) nogil:
""" Returns the minimal distance |spike_time - spike_train[i]|
with i>=start_index.
"""
cdef double d, d_temp
d = fabs(spike_time - spike_train[start_index])
start_index += 1
while start_index < N:
d_temp = fabs(spike_time - spike_train[start_index])
if d_temp > d:
break
else:
d = d_temp
start_index += 1
return d
############################################################
# isi_avrg_cython
############################################################
cdef inline double isi_avrg_cython(double isi1, double isi2) nogil:
return 0.5*(isi1+isi2)*(isi1+isi2)
# alternative definition to obtain <S> ~ 0.5 for Poisson spikes
# return 0.5*(isi1*isi1+isi2*isi2)
############################################################
# spike_distance_cython
############################################################
def spike_distance_cython(double[:] t1,
double[:] t2):
cdef double[:] spike_events
cdef double[:] y_starts
cdef double[:] y_ends
cdef int N1, N2, index1, index2, index
cdef double dt_p1, dt_p2, dt_f1, dt_f2, isi1, isi2, s1, s2
N1 = len(t1)
N2 = len(t2)
spike_events = np.empty(N1+N2-2)
spike_events[0] = t1[0]
y_starts = np.empty(len(spike_events)-1)
y_ends = np.empty(len(spike_events)-1)
with nogil: # release the interpreter to allow multithreading
index1 = 0
index2 = 0
index = 1
dt_p1 = 0.0
dt_f1 = get_min_dist_cython(t1[1], t2, N2, 0)
dt_p2 = 0.0
dt_f2 = get_min_dist_cython(t2[1], t1, N1, 0)
isi1 = max(t1[1]-t1[0], t1[2]-t1[1])
isi2 = max(t2[1]-t2[0], t2[2]-t2[1])
s1 = dt_f1*(t1[1]-t1[0])/isi1
s2 = dt_f2*(t2[1]-t2[0])/isi2
y_starts[0] = (s1*isi2 + s2*isi1) / isi_avrg_cython(isi1, isi2)
while True:
# print(index, index1, index2)
if t1[index1+1] < t2[index2+1]:
index1 += 1
# break condition relies on existence of spikes at T_end
if index1+1 >= N1:
break
spike_events[index] = t1[index1]
# first calculate the previous interval end value
dt_p1 = dt_f1 # the previous time now was the following time before
s1 = dt_p1
s2 = (dt_p2*(t2[index2+1]-t1[index1]) +
dt_f2*(t1[index1]-t2[index2])) / isi2
y_ends[index-1] = (s1*isi2 + s2*isi1)/isi_avrg_cython(isi1, isi2)
# now the next interval start value
dt_f1 = get_min_dist_cython(t1[index1+1], t2, N2, index2)
isi1 = t1[index1+1]-t1[index1]
# s2 is the same as above, thus we can compute y2 immediately
y_starts[index] = (s1*isi2 + s2*isi1)/isi_avrg_cython(isi1, isi2)
elif t1[index1+1] > t2[index2+1]:
index2 += 1
if index2+1 >= N2:
break
spike_events[index] = t2[index2]
# first calculate the previous interval end value
dt_p2 = dt_f2 # the previous time now was the following time before
s1 = (dt_p1*(t1[index1+1]-t2[index2]) +
dt_f1*(t2[index2]-t1[index1])) / isi1
s2 = dt_p2
y_ends[index-1] = (s1*isi2 + s2*isi1) / isi_avrg_cython(isi1, isi2)
# now the next interval start value
dt_f2 = get_min_dist_cython(t2[index2+1], t1, N1, index1)
#s2 = dt_f2
isi2 = t2[index2+1]-t2[index2]
# s2 is the same as above, thus we can compute y2 immediately
y_starts[index] = (s1*isi2 + s2*isi1)/isi_avrg_cython(isi1, isi2)
else: # t1[index1+1] == t2[index2+1] - generate only one event
index1 += 1
index2 += 1
if (index1+1 >= N1) or (index2+1 >= N2):
break
spike_events[index] = t1[index1]
y_ends[index-1] = 0.0
y_starts[index] = 0.0
dt_p1 = 0.0
dt_p2 = 0.0
dt_f1 = get_min_dist_cython(t1[index1+1], t2, N2, index2)
dt_f2 = get_min_dist_cython(t2[index2+1], t1, N1, index1)
isi1 = t1[index1+1]-t1[index1]
isi2 = t2[index2+1]-t2[index2]
index += 1
# the last event is the interval end
spike_events[index] = t1[N1-1]
# the ending value of the last interval
isi1 = max(t1[N1-1]-t1[N1-2], t1[N1-2]-t1[N1-3])
isi2 = max(t2[N2-1]-t2[N2-2], t2[N2-2]-t2[N2-3])
s1 = dt_p1*(t1[N1-1]-t1[N1-2])/isi1
s2 = dt_p2*(t2[N2-1]-t2[N2-2])/isi2
y_ends[index-1] = (s1*isi2 + s2*isi1) / isi_avrg_cython(isi1, isi2)
# 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_python
############################################################
cdef inline double get_tau(double[:] spikes1, double[:] spikes2,
int i, int j, max_tau):
cdef double m = 1E100 # some huge number
cdef int N1 = len(spikes1)-2
cdef int N2 = len(spikes2)-2
if i < N1:
m = fmin(m, spikes1[i+1]-spikes1[i])
if j < N2:
m = fmin(m, spikes2[j+1]-spikes2[j])
if i > 1:
m = fmin(m, spikes1[i]-spikes1[i-1])
if j > 1:
m = fmin(m, spikes2[j]-spikes2[j-1])
m *= 0.5
if max_tau > 0.0:
m = fmin(m, max_tau)
return m
############################################################
# coincidence_cython
############################################################
def coincidence_cython(double[:] spikes1, double[:] spikes2, double max_tau):
cdef int N1 = len(spikes1)
cdef int N2 = len(spikes2)
cdef int i = 0
cdef int j = 0
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 tau
while n < N1 + N2 - 2:
if 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 > 0 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 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 > 0 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
if i == N1-1 or j == N2-1:
break
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] = spikes1[0]
st[len(st)-1] = spikes1[len(spikes1)-1]
c[0] = c[1]
c[len(c)-1] = c[len(c)-2]
mp[0] = mp[1]
mp[len(mp)-1] = mp[len(mp)-2]
return st, c, mp
|
