diff options
Diffstat (limited to 'pyspike/cython')
| -rw-r--r-- | pyspike/cython/__init__.py | 0 | ||||
| -rw-r--r-- | pyspike/cython/cython_add.pyx | 232 | ||||
| -rw-r--r-- | pyspike/cython/cython_directionality.pyx | 262 | ||||
| -rw-r--r-- | pyspike/cython/cython_distances.pyx | 631 | ||||
| -rw-r--r-- | pyspike/cython/cython_profiles.pyx | 485 | ||||
| -rw-r--r-- | pyspike/cython/cython_simulated_annealing.pyx | 82 | ||||
| -rw-r--r-- | pyspike/cython/directionality_python_backend.py | 144 | ||||
| -rw-r--r-- | pyspike/cython/python_backend.py | 638 |
8 files changed, 2474 insertions, 0 deletions
diff --git a/pyspike/cython/__init__.py b/pyspike/cython/__init__.py new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/pyspike/cython/__init__.py diff --git a/pyspike/cython/cython_add.pyx b/pyspike/cython/cython_add.pyx new file mode 100644 index 0000000..25f1181 --- /dev/null +++ b/pyspike/cython/cython_add.pyx @@ -0,0 +1,232 @@ +#cython: boundscheck=False +#cython: wraparound=False +#cython: cdivision=True + +""" +cython_add.pyx + +cython implementation of the add function for piece-wise const and +piece-wise linear functions + +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_add.pyx + +which gives:: + + cython_add.html + +""" + +import numpy as np +cimport numpy as np + +from libc.math cimport fabs + +DTYPE = np.float +ctypedef np.float_t DTYPE_t + + +############################################################ +# add_piece_wise_const_cython +############################################################ +def add_piece_wise_const_cython(double[:] x1, double[:] y1, + double[:] x2, double[:] y2): + + cdef int N1 = len(x1) + cdef int N2 = len(x2) + cdef double[:] x_new = np.empty(N1+N2) + cdef double[:] y_new = np.empty(N1+N2-1) + cdef int index1 = 0 + cdef int index2 = 0 + cdef int index = 0 + cdef int i + with nogil: # release the interpreter lock to allow multi-threading + x_new[0] = x1[0] + y_new[0] = y1[0] + y2[0] + while (index1+1 < N1-1) and (index2+1 < N2-1): + 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 < N1-1: + x_new[index+1:index+1+N1-index1-1] = x1[index1+1:] + for i in xrange(N1-index1-2): + y_new[index+1+i] = y1[index1+1+i] + y2[N2-2] + index += N1-index1-2 + elif index2+1 < N2-1: + x_new[index+1:index+1+N2-index2-1] = x2[index2+1:] + for i in xrange(N2-index2-2): + y_new[index+1+i] = y2[index2+1+i] + y1[N1-2] + index += N2-index2-2 + else: # both arrays reached the end simultaneously + # only the last x-value missing + x_new[index+1] = x1[N1-1] + # end nogil + # return np.asarray(x_new[:index+2]), np.asarray(y_new[:index+1]) + return np.asarray(x_new[:index+2]), np.asarray(y_new[:index+1]) + + +############################################################ +# add_piece_wise_lin_cython +############################################################ +def add_piece_wise_lin_cython(double[:] x1, double[:] y11, double[:] y12, + double[:] x2, double[:] y21, double[:] y22): + cdef int N1 = len(x1) + cdef int N2 = len(x2) + cdef double[:] x_new = np.empty(N1+N2) + cdef double[:] y1_new = np.empty(N1+N2-1) + cdef double[:] y2_new = np.empty_like(y1_new) + cdef int index1 = 0 # index for self + cdef int index2 = 0 # index for f + cdef int index = 0 # index for new + cdef int i + cdef double y + with nogil: # release the interpreter lock to allow multi-threading + x_new[0] = x1[0] + y1_new[0] = y11[0] + y21[0] + while (index1+1 < N1-1) and (index2+1 < N2-1): + # 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 < N1-1: + x_new[index+1:index+1+N1-index1-1] = x1[index1+1:] + for i in xrange(N1-index1-2): + # compute the linear interpolations value + y = y21[index2] + (y22[index2]-y21[index2]) * \ + (x1[index1+1+i]-x2[index2]) / (x2[index2+1]-x2[index2]) + y1_new[index+1+i] = y11[index1+1+i] + y + y2_new[index+i] = y12[index1+i] + y + index += N1-index1-2 + elif index2+1 < N2-1: + x_new[index+1:index+1+N2-index2-1] = x2[index2+1:] + # compute the linear interpolations values + for i in xrange(N2-index2-2): + y = y11[index1] + (y12[index1]-y11[index1]) * \ + (x2[index2+1+i]-x1[index1]) / \ + (x1[index1+1]-x1[index1]) + y1_new[index+1+i] = y21[index2+1+i] + y + y2_new[index+i] = y22[index2+i] + y + index += N2-index2-2 + else: # both arrays reached the end simultaneously + # only the last x-value missing + x_new[index+1] = x1[N1-1] + # finally, the end value for the last interval + y2_new[index] = y12[N1-2]+y22[N2-2] + # only use the data that was actually filled + # end nogil + return (np.asarray(x_new[:index+2]), + np.asarray(y1_new[:index+1]), + np.asarray(y2_new[:index+1])) + + +############################################################ +# add_discrete_function_cython +############################################################ +def add_discrete_function_cython(double[:] x1, double[:] y1, double[:] mp1, + double[:] x2, double[:] y2, double[:] mp2): + + cdef double[:] x_new = np.empty(len(x1) + len(x2)) + cdef double[:] y_new = np.empty_like(x_new) + cdef double[:] mp_new = np.empty_like(x_new) + cdef int index1 = 0 + cdef int index2 = 0 + cdef int index = 0 + cdef int N1 = len(y1)-1 + cdef int N2 = len(y2)-1 + x_new[0] = x1[0] + while (index1+1 < N1) and (index2+1 < N2): + 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 < N1: + x_new[index+1:index+1+N1-index1] = x1[index1+1:] + y_new[index+1:index+1+N1-index1] = y1[index1+1:] + mp_new[index+1:index+1+N1-index1] = mp1[index1+1:] + index += N1-index1 + elif index2+1 < N2: + x_new[index+1:index+1+N2-index2] = x2[index2+1:] + y_new[index+1:index+1+N2-index2] = y2[index2+1:] + mp_new[index+1:index+1+N2-index2] = mp2[index2+1:] + index += N2-index2 + else: # both arrays reached the end simultaneously + x_new[index+1] = x1[index1+1] + y_new[index+1] = y1[index1+1] + y2[index2+1] + mp_new[index+1] = mp1[index1+1] + mp2[index2+1] + index += 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 (np.asarray(x_new[:index+1]), + np.asarray(y_new[:index+1]), + np.asarray(mp_new[:index+1])) diff --git a/pyspike/cython/cython_directionality.pyx b/pyspike/cython/cython_directionality.pyx new file mode 100644 index 0000000..ac37690 --- /dev/null +++ b/pyspike/cython/cython_directionality.pyx @@ -0,0 +1,262 @@ +#cython: boundscheck=False +#cython: wraparound=False +#cython: cdivision=True + +""" +cython_directionality.pyx + +cython implementation of the spike delay asymmetry measures + +Copyright 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_directionality.pyx + +which gives:: + + cython_directionality.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_distances cimport get_tau + +DTYPE = np.float +ctypedef np.float_t DTYPE_t + + +############################################################ +# get_tau +############################################################ +cdef inline double get_tau(double[:] spikes1, double[:] spikes2, + int i, int j, double interval, double max_tau): + cdef double m = interval # use interval length as initial tau + cdef int N1 = spikes1.shape[0]-1 # len(spikes1)-1 + cdef int N2 = spikes2.shape[0]-1 # len(spikes2)-1 + if i < N1 and i > -1: + m = fmin(m, spikes1[i+1]-spikes1[i]) + if j < N2 and j > -1: + m = fmin(m, spikes2[j+1]-spikes2[j]) + if i > 0: + m = fmin(m, spikes1[i]-spikes1[i-1]) + if j > 0: + m = fmin(m, spikes2[j]-spikes2[j-1]) + m *= 0.5 + if max_tau > 0.0: + m = fmin(m, max_tau) + return m + + +############################################################ +# spike_train_order_profile_cython +############################################################ +def spike_train_order_profile_cython(double[:] spikes1, double[:] spikes2, + double t_start, double t_end, + double max_tau): + + 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[:] a = np.zeros(N1 + N2 + 2) # asymmetry values + cdef double[:] mp = np.ones(N1 + N2 + 2) # multiplicity + cdef double interval = t_end - t_start + cdef double 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, interval, max_tau) + st[n] = spikes1[i] + if j > -1 and spikes1[i]-spikes2[j] < tau: + # coincidence between the current spike and the previous spike + # spike from spike train 1 after spike train 2 + # both get marked with -1 + a[n] = -1 + a[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, interval, max_tau) + st[n] = spikes2[j] + if i > -1 and spikes2[j]-spikes1[i] < tau: + # coincidence between the current spike and the previous spike + # spike from spike train 1 before spike train 2 + # both get marked with 1 + a[n] = 1 + a[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 with zero asymmetry value and multiplicity 2 + st[n] = spikes1[i] + a[n] = 0 + mp[n] = 2 + + st = st[:n+2] + a = a[:n+2] + mp = mp[:n+2] + + st[0] = t_start + st[len(st)-1] = t_end + if N1 + N2 > 0: + a[0] = a[1] + a[len(a)-1] = a[len(a)-2] + mp[0] = mp[1] + mp[len(mp)-1] = mp[len(mp)-2] + else: + a[0] = 1 + a[1] = 1 + + return st, a, mp + + +############################################################ +# spike_train_order_cython +############################################################ +def spike_train_order_cython(double[:] spikes1, double[:] spikes2, + double t_start, double t_end, double max_tau): + + cdef int N1 = len(spikes1) + cdef int N2 = len(spikes2) + cdef int i = -1 + cdef int j = -1 + cdef int d = 0 + cdef int mp = 0 + cdef double interval = t_end - t_start + cdef double tau + while i + j < N1 + N2 - 2: + if (i < N1-1) and (j == N2-1 or spikes1[i+1] < spikes2[j+1]): + i += 1 + mp += 1 + tau = get_tau(spikes1, spikes2, i, j, interval, max_tau) + if j > -1 and spikes1[i]-spikes2[j] < tau: + # coincidence between the current spike and the previous spike + # spike in spike train 2 appeared before spike in spike train 1 + # mark with -1 + d -= 2 + elif (j < N2-1) and (i == N1-1 or spikes1[i+1] > spikes2[j+1]): + j += 1 + mp += 1 + tau = get_tau(spikes1, spikes2, i, j, interval, max_tau) + if i > -1 and spikes2[j]-spikes1[i] < tau: + # coincidence between the current spike and the previous spike + # spike in spike train 1 appeared before spike in spike train 2 + # mark with +1 + d += 2 + else: # spikes1[i+1] = spikes2[j+1] + # advance in both spike trains + j += 1 + i += 1 + # add only one event with multiplicity 2, but no asymmetry counting + mp += 2 + + if d == 0 and mp == 0: + # empty spike trains -> spike sync = 1 by definition + d = 1 + mp = 1 + + return d, mp + + +############################################################ +# spike_directionality_profiles_cython +############################################################ +def spike_directionality_profiles_cython(double[:] spikes1, + double[:] spikes2, + double t_start, double t_end, + double max_tau): + + cdef int N1 = len(spikes1) + cdef int N2 = len(spikes2) + cdef int i = -1 + cdef int j = -1 + cdef double[:] d1 = np.zeros(N1) # directionality values + cdef double[:] d2 = np.zeros(N2) # directionality values + cdef double interval = t_end - t_start + cdef double tau + while i + j < N1 + N2 - 2: + if (i < N1-1) and (j == N2-1 or spikes1[i+1] < spikes2[j+1]): + i += 1 + tau = get_tau(spikes1, spikes2, i, j, interval, max_tau) + if j > -1 and spikes1[i]-spikes2[j] < tau: + # coincidence between the current spike and the previous spike + # spike from spike train 1 after spike train 2 + # leading spike gets +1, following spike -1 + d1[i] = -1 + d2[j] = +1 + elif (j < N2-1) and (i == N1-1 or spikes1[i+1] > spikes2[j+1]): + j += 1 + tau = get_tau(spikes1, spikes2, i, j, interval, max_tau) + if i > -1 and spikes2[j]-spikes1[i] < tau: + # coincidence between the current spike and the previous spike + # spike from spike train 1 before spike train 2 + # leading spike gets +1, following spike -1 + d1[i] = +1 + d2[j] = -1 + else: # spikes1[i+1] = spikes2[j+1] + # advance in both spike trains + j += 1 + i += 1 + # equal spike times: zero asymmetry value + d1[i] = 0 + d2[j] = 0 + + return d1, d2 + + +############################################################ +# spike_directionality_cython +############################################################ +def spike_directionality_cython(double[:] spikes1, + double[:] spikes2, + double t_start, double t_end, + double max_tau): + + cdef int N1 = len(spikes1) + cdef int N2 = len(spikes2) + cdef int i = -1 + cdef int j = -1 + cdef int d = 0 # directionality value + cdef double interval = t_end - t_start + cdef double tau + while i + j < N1 + N2 - 2: + if (i < N1-1) and (j == N2-1 or spikes1[i+1] < spikes2[j+1]): + i += 1 + tau = get_tau(spikes1, spikes2, i, j, interval, max_tau) + if j > -1 and spikes1[i]-spikes2[j] < tau: + # coincidence between the current spike and the previous spike + # spike from spike train 1 after spike train 2 + # leading spike gets +1, following spike -1 + d -= 1 + elif (j < N2-1) and (i == N1-1 or spikes1[i+1] > spikes2[j+1]): + j += 1 + tau = get_tau(spikes1, spikes2, i, j, interval, max_tau) + if i > -1 and spikes2[j]-spikes1[i] < tau: + # coincidence between the current spike and the previous spike + # spike from spike train 1 before spike train 2 + # leading spike gets +1, following spike -1 + d += 1 + else: # spikes1[i+1] = spikes2[j+1] + # advance in both spike trains + j += 1 + i += 1 + + return d diff --git a/pyspike/cython/cython_distances.pyx b/pyspike/cython/cython_distances.pyx new file mode 100644 index 0000000..d4070ae --- /dev/null +++ b/pyspike/cython/cython_distances.pyx @@ -0,0 +1,631 @@ +#cython: boundscheck=False +#cython: wraparound=False +#cython: cdivision=True + +""" +cython_distances.pyx + +cython implementation of the isi-, spike- and spike-sync distances + +Note: using cython memoryviews (e.g. double[:]) instead of ndarray objects +improves the performance of spike_distance by a factor of 10! + +Copyright 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_distances.pyx + +which gives:: + + cython_distances.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, + double t_start, double t_end): + + cdef double isi_value + cdef int index1, index2, index + cdef int N1, N2 + cdef double nu1, nu2 + cdef double last_t, curr_t, curr_isi + isi_value = 0.0 + N1 = len(s1) + N2 = len(s2) + + # first interspike interval - check if a spike exists at the start time + # and also account for spike trains with single spikes + if s1[0] > t_start: + # edge correction for the first interspike interval: + # take the maximum of the distance from the beginning to the first + # spike and the interval between the first two spikes. + # if there is only one spike, take the its distance to the beginning + nu1 = fmax(s1[0]-t_start, s1[1]-s1[0]) if N1 > 1 else s1[0]-t_start + index1 = -1 + else: + # if the first spike is exactly at the start, take the distance + # to the next spike. If this is the only spike, take the distance to + # the end. + nu1 = s1[1]-s1[0] if N1 > 1 else t_end-s1[0] + index1 = 0 + + if s2[0] > t_start: + # edge correction as above + 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 + + last_t = t_start + curr_isi = fabs(nu1-nu2)/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 + curr_t = s1[index1] + if index1 < N1-1: + nu1 = s1[index1+1]-s1[index1] + else: + # edge correction for the last ISI: + # take the max of the distance of the last + # spike to the end and the previous ISI. If there was only + # one spike, always take the distance to the end. + 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 + curr_t = s2[index2] + if index2 < N2-1: + nu2 = s2[index2+1]-s2[index2] + else: + # edge correction for the end as above + 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 + curr_t = s1[index1] + if index1 < N1-1: + nu1 = s1[index1+1]-s1[index1] + else: + # edge correction for the end as above + 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 for the end as above + nu2 = fmax(t_end-s2[index2], nu2) if N2 > 1 \ + else t_end-s2[index2] + # compute the corresponding isi-distance + isi_value += curr_isi * (curr_t - last_t) + curr_isi = fabs(nu1 - nu2) / fmax(nu1, nu2) + last_t = curr_t + index += 1 + + isi_value += curr_isi * (t_end - last_t) + # end nogil + + return isi_value / (t_end-t_start) + + +############################################################ +# 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 + + +############################################################ +# 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) + # another alternative definition without second normalization + # return 0.5*(isi1+isi2) + + +############################################################ +# spike_distance_cython +############################################################ +def spike_distance_cython(double[:] t1, double[:] t2, + double t_start, double t_end): + + 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 + cdef double y_start, y_end, t_last, t_current, spike_value + cdef double[:] t_aux1 = np.empty(2) + cdef double[:] t_aux2 = np.empty(2) + + spike_value = 0.0 + + N1 = len(t1) + N2 = len(t2) + + # we can assume at least one spikes per spike train + assert N1 > 0 + assert N2 > 0 + + + with nogil: # release the interpreter to allow multithreading + t_last = 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 + # print "aux spikes %.15f, %.15f ; %.15f, %.15f" % (t_aux1[0], t_aux1[1], t_aux2[0], t_aux2[1]) + 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: # t1[0] == t_start + 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: # t2[0] == t_start + 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 = t_start-t_p1 # 0.0 + 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_start = (s1*isi2 + s2*isi1) / isi_avrg_cython(isi1, isi2) + # alternative definition without second normalization + # y_start = (s1 + s2) / isi_avrg_cython(isi1, isi2) + 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] + t_curr = t_p1 + s2 = (dt_p2*(t_f2-t_p1) + dt_f2*(t_p1-t_p2)) / isi2 + y_end = (s1*isi2 + s2*isi1)/isi_avrg_cython(isi1, isi2) + # alternative definition without second normalization + # y_end = (s1 + s2) / isi_avrg_cython(isi1, isi2) + + spike_value += 0.5*(y_start + y_end) * (t_curr - t_last) + + # 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_start = (s1*isi2 + s2*isi1)/isi_avrg_cython(isi1, isi2) + # alternative definition without second normalization + # y_start = (s1 + s2) / isi_avrg_cython(isi1, isi2) + 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] + t_curr = t_p2 + s1 = (dt_p1*(t_f1-t_p2) + dt_f1*(t_p2-t_p1)) / isi1 + y_end = (s1*isi2 + s2*isi1) / isi_avrg_cython(isi1, isi2) + # alternative definition without second normalization + # y_end = (s1 + s2) / isi_avrg_cython(isi1, isi2) + + spike_value += 0.5*(y_start + y_end) * (t_curr - t_last) + + # 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 + # s1 is the same as above, thus we can compute y2 immediately + y_start = (s1*isi2 + s2*isi1)/isi_avrg_cython(isi1, isi2) + # alternative definition without second normalization + # y_start = (s1 + s2) / isi_avrg_cython(isi1, isi2) + + 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 + t_curr = t_f1 + y_end = 0.0 + spike_value += 0.5*(y_start + y_end) * (t_curr - t_last) + y_start = 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 + t_last = t_curr + # 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_end = (s1*isi2 + s2*isi1) / isi_avrg_cython(isi1, isi2) + # alternative definition without second normalization + # y_end = (s1 + s2) / isi_avrg_cython(isi1, isi2) + + spike_value += 0.5*(y_start + y_end) * (t_end - t_last) + # end nogil + + # use only the data added above + # could be less than original length due to equal spike times + return spike_value / (t_end-t_start) + + +############################################################ +# isi_avrg_rf_cython +############################################################ +cdef inline double isi_avrg_rf_cython(double isi1, double isi2) nogil: + # rate free version + return (isi1+isi2) + + +############################################################ +# spike_distance_rf_cython +############################################################ +def spike_distance_rf_cython(double[:] t1, double[:] t2, + double t_start, double t_end): + + 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 + cdef double y_start, y_end, t_last, t_current, spike_value + + spike_value = 0.0 + + N1 = len(t1) + N2 = len(t2) + + with nogil: # release the interpreter to allow multithreading + t_last = t_start + t_p1 = t_start + t_p2 = t_start + 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_start, t_end) + isi1 = fmax(t_f1-t_start, t1[1]-t1[0]) + dt_p1 = dt_f1 + s1 = dt_p1*(t_f1-t_start)/isi1 + index1 = -1 + else: + t_f1 = t1[1] + dt_f1 = get_min_dist_cython(t_f1, t2, N2, 0, t_start, t_end) + dt_p1 = 0.0 + 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_cython(t_f2, t1, N1, 0, t_start, t_end) + dt_p2 = dt_f2 + isi2 = fmax(t_f2-t_start, t2[1]-t2[0]) + s2 = dt_p2*(t_f2-t_start)/isi2 + index2 = -1 + else: + t_f2 = t2[1] + dt_f2 = get_min_dist_cython(t_f2, t1, N1, 0, t_start, t_end) + dt_p2 = 0.0 + isi2 = t2[1]-t2[0] + s2 = dt_p2 + index2 = 0 + + # y_start = (s1*isi2 + s2*isi1) / isi_avrg_cython(isi1, isi2) + # alternative definition without second normalization + y_start = (s1 + s2) / isi_avrg_rf_cython(isi1, isi2) + 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 + t_curr = t_p1 + s2 = (dt_p2*(t_f2-t_p1) + dt_f2*(t_p1-t_p2)) / isi2 + # y_end = (s1*isi2 + s2*isi1)/isi_avrg_cython(isi1, isi2) + # alternative definition without second normalization + y_end = (s1 + s2) / isi_avrg_rf_cython(isi1, isi2) + + spike_value += 0.5*(y_start + y_end) * (t_curr - t_last) + + # now the next interval start value + if index1 < N1-1: + dt_f1 = get_min_dist_cython(t_f1, t2, N2, index2, + t_start, t_end) + 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]) + # 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_start = (s1*isi2 + s2*isi1)/isi_avrg_cython(isi1, isi2) + # alternative definition without second normalization + y_start = (s1 + s2) / isi_avrg_rf_cython(isi1, isi2) + 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_end + t_curr = t_p2 + s1 = (dt_p1*(t_f1-t_p2) + dt_f1*(t_p2-t_p1)) / isi1 + # y_end = (s1*isi2 + s2*isi1) / isi_avrg_cython(isi1, isi2) + # alternative definition without second normalization + y_end = (s1 + s2) / isi_avrg_rf_cython(isi1, isi2) + + spike_value += 0.5*(y_start + y_end) * (t_curr - t_last) + + # now the next interval start value + if index2 < N2-1: + dt_f2 = get_min_dist_cython(t_f2, t1, N1, index1, + t_start, t_end) + 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]) + # s2 needs adjustment due to change of isi2 + s2 = dt_p2*(t_end-t2[N2-1])/isi2 + # s1 is the same as above, thus we can compute y2 immediately + # y_start = (s1*isi2 + s2*isi1)/isi_avrg_cython(isi1, isi2) + # alternative definition without second normalization + y_start = (s1 + s2) / isi_avrg_rf_cython(isi1, isi2) + + 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 + t_curr = t_f1 + y_end = 0.0 + spike_value += 0.5*(y_start + y_end) * (t_curr - t_last) + y_start = 0.0 + if index1 < N1-1: + t_f1 = t1[index1+1] + dt_f1 = get_min_dist_cython(t_f1, t2, N2, index2, + t_start, t_end) + isi1 = t_f1 - t_p1 + else: + t_f1 = t_end + dt_f1 = dt_p1 + isi1 = fmax(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_cython(t_f2, t1, N1, index1, + t_start, t_end) + isi2 = t_f2 - t_p2 + else: + t_f2 = t_end + dt_f2 = dt_p2 + isi2 = fmax(t_end-t2[N2-1], t2[N2-1]-t2[N2-2]) + index += 1 + t_last = t_curr + # 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_end = (s1*isi2 + s2*isi1) / isi_avrg_cython(isi1, isi2) + # alternative definition without second normalization + y_end = (s1 + s2) / isi_avrg_rf_cython(isi1, isi2) + + spike_value += 0.5*(y_start + y_end) * (t_end - t_last) + # end nogil + + # use only the data added above + # could be less than original length due to equal spike times + return spike_value / (t_end-t_start) + + + +############################################################ +# get_tau +############################################################ +cdef inline double get_tau(double[:] spikes1, double[:] spikes2, + int i, int j, double interval, double max_tau): + cdef double m = interval # use interval length as initial tau + cdef int N1 = spikes1.shape[0]-1 # len(spikes1)-1 + cdef int N2 = spikes2.shape[0]-1 # len(spikes2)-1 + if i < N1 and i > -1: + m = fmin(m, spikes1[i+1]-spikes1[i]) + if j < N2 and j > -1: + m = fmin(m, spikes2[j+1]-spikes2[j]) + if i > 0: + m = fmin(m, spikes1[i]-spikes1[i-1]) + if j > 0: + m = fmin(m, spikes2[j]-spikes2[j-1]) + m *= 0.5 + if max_tau > 0.0: + m = fmin(m, max_tau) + return m + + +############################################################ +# coincidence_value_cython +############################################################ +def coincidence_value_cython(double[:] spikes1, double[:] spikes2, + double t_start, double t_end, double max_tau): + + cdef int N1 = len(spikes1) + cdef int N2 = len(spikes2) + cdef int i = -1 + cdef int j = -1 + cdef double coinc = 0.0 + cdef double mp = 0.0 + cdef double interval = t_end - t_start + cdef double tau + while i + j < N1 + N2 - 2: + if (i < N1-1) and (j == N2-1 or spikes1[i+1] < spikes2[j+1]): + i += 1 + mp += 1 + tau = get_tau(spikes1, spikes2, i, j, interval, max_tau) + if j > -1 and spikes1[i]-spikes2[j] < tau: + # coincidence between the current spike and the previous spike + # both get marked with 1 + coinc += 2 + elif (j < N2-1) and (i == N1-1 or spikes1[i+1] > spikes2[j+1]): + j += 1 + mp += 1 + tau = get_tau(spikes1, spikes2, i, j, interval, max_tau) + if i > -1 and spikes2[j]-spikes1[i] < tau: + # coincidence between the current spike and the previous spike + # both get marked with 1 + coinc += 2 + else: # spikes1[i+1] = spikes2[j+1] + # advance in both spike trains + j += 1 + i += 1 + # add only one event, but with coincidence 2 and multiplicity 2 + mp += 2 + coinc += 2 + + return coinc, mp diff --git a/pyspike/cython/cython_profiles.pyx b/pyspike/cython/cython_profiles.pyx new file mode 100644 index 0000000..aa24db4 --- /dev/null +++ b/pyspike/cython/cython_profiles.pyx @@ -0,0 +1,485 @@ +#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 + +DTYPE = np.float +ctypedef np.float_t DTYPE_t + + +############################################################ +# isi_profile_cython +############################################################ +def isi_profile_cython(double[:] s1, double[:] s2, + double t_start, double t_end): + + 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(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(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 + + +############################################################ +# 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_profile_cython +############################################################ +def spike_profile_cython(double[:] t1, double[:] t2, + double t_start, double t_end): + + 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] = (s1*isi2 + s2*isi1) / isi_avrg_cython(isi1, isi2) + 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] = (s1*isi2 + s2*isi1)/isi_avrg_cython(isi1, + isi2) + # 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] = (s1*isi2 + s2*isi1)/isi_avrg_cython(isi1, + isi2) + 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] = (s1*isi2 + s2*isi1) / isi_avrg_cython(isi1, + isi2) + # 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] = (s1*isi2 + s2*isi1)/isi_avrg_cython(isi1, isi2) + 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] = (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] + + + +############################################################ +# get_tau +############################################################ +cdef inline double get_tau(double[:] spikes1, double[:] spikes2, + int i, int j, double interval, double max_tau): + cdef double m = interval # use interval as initial tau + cdef int N1 = spikes1.shape[0]-1 # len(spikes1)-1 + cdef int N2 = spikes2.shape[0]-1 # len(spikes2)-1 + if i < N1 and i > -1: + m = fmin(m, spikes1[i+1]-spikes1[i]) + if j < N2 and j > -1: + m = fmin(m, spikes2[j+1]-spikes2[j]) + if i > 0: + m = fmin(m, spikes1[i]-spikes1[i-1]) + if j > 0: + m = fmin(m, spikes2[j]-spikes2[j-1]) + m *= 0.5 + if max_tau > 0.0: + m = fmin(m, max_tau) + return m + + +############################################################ +# coincidence_profile_cython +############################################################ +def coincidence_profile_cython(double[:] spikes1, double[:] spikes2, + double t_start, double t_end, double max_tau): + + 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 + 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, interval, 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, interval, 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 + + +############################################################ +# coincidence_single_profile_cython +############################################################ +def coincidence_single_profile_cython(double[:] spikes1, double[:] spikes2, + double t_start, double t_end, double max_tau): + + 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 + 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, interval, max_tau) + 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, interval, max_tau) + if fabs(spikes2[j]-spikes1[i]) < tau: + # current spike in st1 is coincident + c[i] = 1 + return c diff --git a/pyspike/cython/cython_simulated_annealing.pyx b/pyspike/cython/cython_simulated_annealing.pyx new file mode 100644 index 0000000..be9423c --- /dev/null +++ b/pyspike/cython/cython_simulated_annealing.pyx @@ -0,0 +1,82 @@ +#cython: boundscheck=False +#cython: wraparound=False +#cython: cdivision=True + +""" +cython_simulated_annealing.pyx + +cython implementation of a simulated annealing algorithm to find the optimal +spike train order + +Note: using cython memoryviews (e.g. double[:]) instead of ndarray objects +improves the performance of spike_distance by a factor of 10! + +Copyright 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_simulated_annealing.pyx + +which gives: + + cython_simulated_annealing.html + +""" + +import numpy as np +cimport numpy as np + +from libc.math cimport exp +from libc.math cimport fmod +from libc.stdlib cimport rand +from libc.stdlib cimport RAND_MAX + +DTYPE = np.float +ctypedef np.float_t DTYPE_t + + +def sim_ann_cython(double[:, :] D, double T_start, double T_end, double alpha): + + cdef long N = len(D) + cdef double A = np.sum(np.triu(D, 0)) + cdef long[:] p = np.arange(N) + cdef double T = T_start + cdef long iterations + cdef long succ_iter + cdef long total_iter = 0 + cdef double delta_A + cdef long ind1 + cdef long ind2 + + while T > T_end: + iterations = 0 + succ_iter = 0 + # equilibrate for 100*N steps or 10*N successful steps + while iterations < 100*N and succ_iter < 10*N: + # exchange two rows and cols + # ind1 = np.random.randint(N-1) + ind1 = rand() % (N-1) + if ind1 < N-1: + ind2 = ind1+1 + else: # this can never happen! + ind2 = 0 + delta_A = -2*D[p[ind1], p[ind2]] + if delta_A > 0.0 or exp(delta_A/T) > ((1.0*rand()) / RAND_MAX): + # swap indices + p[ind1], p[ind2] = p[ind2], p[ind1] + A += delta_A + succ_iter += 1 + iterations += 1 + total_iter += iterations + T *= alpha # cool down + if succ_iter == 0: + # no successful step -> we believe we have converged + break + + return p, A, total_iter diff --git a/pyspike/cython/directionality_python_backend.py b/pyspike/cython/directionality_python_backend.py new file mode 100644 index 0000000..c1d820b --- /dev/null +++ b/pyspike/cython/directionality_python_backend.py @@ -0,0 +1,144 @@ +""" directionality_python_backend.py + +Collection of python functions that can be used instead of the cython +implementation. + +Copyright 2015, Mario Mulansky <mario.mulansky@gmx.net> + +Distributed under the BSD License + +""" + +import numpy as np + + +############################################################ +# spike_train_order_python +############################################################ +def spike_directionality_profile_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 + d1 = np.zeros(N1) # directionality values + d2 = np.zeros(N2) # directionality values + while i + j < N1 + N2 - 2: + if (i < N1-1) and (j == N2-1 or spikes1[i+1] < spikes2[j+1]): + i += 1 + tau = get_tau(spikes1, spikes2, i, j, max_tau) + if j > -1 and spikes1[i]-spikes2[j] < tau: + # coincidence between the current spike and the previous spike + # spike in first spike train occurs after second + d1[i] = -1 + d2[j] = +1 + elif (j < N2-1) and (i == N1-1 or spikes1[i+1] > spikes2[j+1]): + j += 1 + tau = get_tau(spikes1, spikes2, i, j, max_tau) + if i > -1 and spikes2[j]-spikes1[i] < tau: + # coincidence between the current spike and the previous spike + # spike in second spike train occurs after first + d1[i] = +1 + d2[j] = -1 + else: # spikes1[i+1] = spikes2[j+1] + # advance in both spike trains + j += 1 + i += 1 + d1[i] = 0 + d2[j] = 0 + + return d1, d2 + + +############################################################ +# spike_train_order_python +############################################################ +def spike_train_order_profile_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 + a = 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 + a[n] = -1 + a[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 + a[n] = 1 + a[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 with zero asymmetry value and multiplicity 2 + st[n] = spikes1[i] + a[n] = 0 + mp[n] = 2 + + st = st[:n+2] + a = a[:n+2] + mp = mp[:n+2] + + st[0] = t_start + st[len(st)-1] = t_end + if N1 + N2 > 0: + a[0] = a[1] + a[len(a)-1] = a[len(a)-2] + mp[0] = mp[1] + mp[len(mp)-1] = mp[len(mp)-2] + else: + a[0] = 1 + a[1] = 1 + + return st, a, mp diff --git a/pyspike/cython/python_backend.py b/pyspike/cython/python_backend.py new file mode 100644 index 0000000..e75f181 --- /dev/null +++ b/pyspike/cython/python_backend.py @@ -0,0 +1,638 @@ +""" python_backend.py + +Collection of python functions that can be used instead of the cython +implementation. + +Copyright 2014-2015, 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]) 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 = max(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] = 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]) if N1 > 1 \ + else t_end-s1[N1-1] + + 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]) if N2 > 1 \ + else t_end-s2[N2-1] + + 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 N1 > 1 \ + else t_end-s1[N1-1] + 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]) if N2 > 1 \ + else t_end-s2[N2-1] + # 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) + + t_aux1 = np.zeros(2) + t_aux2 = np.zeros(2) + t_aux1[0] = min(t_start, t1[0]-(t1[1]-t1[0])) if N1 > 1 else t_start + t_aux1[1] = max(t_end, t1[N1-1]+(t1[N1-1]-t1[N1-2])) if N1 > 1 else t_end + t_aux2[0] = min(t_start, t2[0]-(t2[1]-t2[0])) if N2 > 1 else t_start + t_aux2[1] = max(t_end, t2[N2-1]+(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] + + # print "t_aux1", t_aux1, ", t_aux2:", t_aux2 + + spike_events[0] = t_start + if t1[0] > t_start: + t_f1 = t1[0] + dt_f1 = get_min_dist(t_f1, t2, 0, t_aux2[0], t_aux2[1]) + dt_p1 = dt_f1 + isi1 = max(t_f1-t_start, t1[1]-t1[0]) if N1 > 1 else t_f1-t_start + # s1 = dt_p1*(t_f1-t_start)/isi1 + s1 = dt_p1 + index1 = -1 + else: + # dt_p1 = t_start-t_p2 + t_f1 = t1[1] if N1 > 1 else t_end + dt_p1 = get_min_dist(t_p1, t2, 0, t_aux2[0], t_aux2[1]) + dt_f1 = get_min_dist(t_f1, t2, 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(t_f2, t1, 0, t_aux1[0], t_aux1[1]) + dt_p2 = dt_f2 + isi2 = max(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_p2 = get_min_dist(t_p2, t1, 0, t_aux1[0], t_aux1[1]) + dt_f2 = get_min_dist(t_f2, t1, 0, t_aux1[0], t_aux1[1]) + isi2 = t_f2-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_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] = (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_aux2[0], t_aux2[1]) + 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]) 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] = (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_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] = (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_aux1[0], t_aux1[1]) + 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]) 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 adjustment: no correction + s2 = dt_p2 + # 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_aux2[0], t_aux2[1]) + isi1 = t_f1 - t_p1 + else: + t_f1 = t_aux1[1] + dt_f1 = dt_p1 + isi1 = max(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(t_f2, t1, index1, t_aux1[0], t_aux1[1]) + isi2 = t_f2 - t_p2 + else: + t_f2 = t_aux2[1] + dt_f2 = dt_p2 + isi2 = max(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 # *(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 + + +def get_tau(spikes1, spikes2, i, j, max_tau, init_tau): + m = init_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 + + +############################################################ +# coincidence_python +############################################################ +def coincidence_python(spikes1, spikes2, t_start, t_end, max_tau): + + 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, t_end-t_start) + 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, t_end-t_start) + 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_python(spikes1, spikes2, t_start, t_end, max_tau): + + N1 = len(spikes1) + N2 = len(spikes2) + j = -1 + c = np.zeros(N1) # coincidences + for i in range(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, max_tau, t_end-t_start) + if j > -1 and abs(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 first or + # 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, max_tau, t_end-t_start) + if abs(spikes2[j]-spikes1[i]) < tau: + # current spike in st1 is coincident + c[i] = 1 + return c + + +############################################################ +# 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 + N1 = len(x1)-1 + N2 = len(x2)-1 + while (index1+1 < N1) and (index2+1 < N2): + 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 < N1: + x_new[index+1:index+1+N1-index1] = x1[index1+1:] + y_new[index+1:index+1+N1-index1] = y1[index1+1:] + mp_new[index+1:index+1+N1-index1] = mp1[index1+1:] + index += N1-index1 + elif index2+1 < N2: + x_new[index+1:index+1+N2-index2] = x2[index2+1:] + y_new[index+1:index+1+N2-index2] = y2[index2+1:] + mp_new[index+1:index+1+N2-index2] = mp2[index2+1:] + index += N2-index2 + 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] + index += 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] |