# pyspike package¶

## Classes¶

### SpikeTrain¶

class pyspike.SpikeTrain.SpikeTrain(spike_times, edges, is_sorted=True)[source]

Bases: object

Class representing spike trains for the PySpike Module.

__init__(spike_times, edges, is_sorted=True)[source]

Constructs the SpikeTrain.

Parameters
• spike_times – ordered array of spike times.

• edges – The edges of the spike train. Given as a pair of floats (T0, T1) or a single float T1, where then T0=0 is assumed.

• is_sorted – If False, the spike times will sorted by np.sort.

copy()[source]

Returns a copy of this spike train. Use this function if you want to create a real (deep) copy of this spike train. Simple assignment t2 = t1 does not create a copy of the spike train data, but a reference as numpy.array is used for storing the data.

Returns

SpikeTrain copy of this spike train.

get_spikes_non_empty()[source]

Returns the spikes of this spike train with auxiliary spikes in case of empty spike trains.

sort()[source]

Sorts the spike times of this spike train using np.sort

### PieceWiseConstFunc¶

class pyspike.PieceWiseConstFunc.PieceWiseConstFunc(x, y)[source]

Bases: object

A class representing a piece-wise constant function.

__init__(x, y)[source]

Constructs the piece-wise const function.

Parameters
• x – array of length N+1 defining the edges of the intervals of the pwc function.

• y – array of length N defining the function values at the intervals.

Adds another PieceWiseConst function to this function. Note: only functions defined on the same interval can be summed.

Parameters

fPieceWiseConstFunc function to be added.

Return type

None

almost_equal(other, decimal=14)[source]

Checks if the function is equal to another function up to decimal precision.

Parameters

other – another PieceWiseConstFunc

Returns

True if the two functions are equal up to decimal decimals, False otherwise

Return type

bool

avrg(interval=None)[source]

Computes the average of the piece-wise const function: $$a = 1/T \int_0^T f(x) dx$$ where T is the length of the interval.

Parameters

interval (Pair, sequence of pairs, or None.) – averaging interval given as a pair of floats, a sequence of pairs for averaging multiple intervals, or None, if None the average over the whole function is computed.

Returns

the average a.

Return type

float

copy()[source]

Returns a copy of itself

Return type

PieceWiseConstFunc

get_plottable_data()[source]

Returns two arrays containing x- and y-coordinates for immeditate plotting of the piece-wise function.

Returns

(x_plot, y_plot) containing plottable data

Return type

pair of np.array

Example:

x, y = f.get_plottable_data()
plt.plot(x, y, '-o', label="Piece-wise const function")

integral(interval=None)[source]

Returns the integral over the given interval.

Parameters

interval (Pair of floats or None.) – integration interval given as a pair of floats, if None the integral over the whole function is computed.

Returns

the integral

Return type

float

mul_scalar(fac)[source]

Multiplies the function with a scalar value

Parameters

fac (double) – Value to multiply

Return type

None

### PieceWiseLinFunc¶

class pyspike.PieceWiseLinFunc.PieceWiseLinFunc(x, y1, y2)[source]

Bases: object

A class representing a piece-wise linear function.

__init__(x, y1, y2)[source]

Constructs the piece-wise linear function.

Parameters
• x – array of length N+1 defining the edges of the intervals of the pwc function.

• y1 – array of length N defining the function values at the left of the intervals.

• y2 – array of length N defining the function values at the right of the intervals.

Adds another PieceWiseLin function to this function. Note: only functions defined on the same interval can be summed.

Parameters

fPieceWiseLinFunc function to be added.

Return type

None

almost_equal(other, decimal=14)[source]

Checks if the function is equal to another function up to decimal precision.

Parameters

other – another PieceWiseLinFunc

Returns

True if the two functions are equal up to decimal decimals, False otherwise

Return type

bool

avrg(interval=None)[source]

Computes the average of the piece-wise linear function: $$a = 1/T \int_0^T f(x) dx$$ where T is the interval length.

Parameters

interval (Pair, sequence of pairs, or None.) – averaging interval given as a pair of floats, a sequence of pairs for averaging multiple intervals, or None, if None the average over the whole function is computed.

Returns

the average a.

Return type

float

copy()[source]

Returns a copy of itself

Return type

PieceWiseLinFunc

get_plottable_data()[source]

Returns two arrays containing x- and y-coordinates for immeditate plotting of the piece-wise function.

Returns

(x_plot, y_plot) containing plottable data

Return type

pair of np.array

Example:

x, y = f.get_plottable_data()
plt.plot(x, y, '-o', label="Piece-wise const function")

integral(interval=None)[source]

Returns the integral over the given interval.

Parameters

interval (Pair of floats or None.) – integration interval given as a pair of floats, if None the integral over the whole function is computed.

Returns

the integral

Return type

float

mul_scalar(fac)[source]

Multiplies the function with a scalar value

Parameters

fac (double) – Value to multiply

Return type

None

### DiscreteFunc¶

class pyspike.DiscreteFunc.DiscreteFunc(x, y, multiplicity)[source]

Bases: object

A class representing values defined on a discrete set of points.

__init__(x, y, multiplicity)[source]

Constructs the discrete function.

Parameters
• x – array of length N defining the points at which the values are defined.

• y – array of length N degining the values at the points x.

• multiplicity – array of length N defining the multiplicity of the values.

Adds another DiscreteFunc function to this function. Note: only functions defined on the same interval can be summed.

Parameters

fDiscreteFunc function to be added.

Return type

None

almost_equal(other, decimal=14)[source]

Checks if the function is equal to another function up to decimal precision.

Parameters

other – another DiscreteFunc

Returns

True if the two functions are equal up to decimal decimals, False otherwise

Return type

bool

avrg(interval=None, normalize=True)[source]

Computes the average of the interval sequence: $$a = 1/N \sum f_n$$ where N is the number of intervals.

Parameters

interval (Pair, sequence of pairs, or None.) – averaging interval given as a pair of floats, a sequence of pairs for averaging multiple intervals, or None, if None the average over the whole function is computed.

Returns

the average a.

Return type

float

copy()[source]

Returns a copy of itself

Return type

DiscreteFunc

get_plottable_data(averaging_window_size=0)[source]

Returns two arrays containing x- and y-coordinates for plotting the interval sequence. The optional parameter averaging_window_size determines the size of an averaging window to smoothen the profile. If this value is 0, no averaging is performed.

Parameters

averaging_window_size – size of the averaging window, default=0.

Returns

(x_plot, y_plot) containing plottable data

Return type

pair of np.array

Example:

x, y = f.get_plottable_data()
plt.plot(x, y, '-o', label="Discrete function")

integral(interval=None)[source]

Returns the integral over the given interval. For the discrete function, this amounts to two values: the sum over all values and the sum over all multiplicities.

Parameters

interval (Pair, sequence of pairs, or None.) – integration interval given as a pair of floats, or a sequence of pairs in case of multiple intervals, if None the integral over the whole function is computed.

Returns

the summed values and the summed multiplicity

Return type

pair of float

mul_scalar(fac)[source]

Multiplies the function with a scalar value

Parameters

fac (double) – Value to multiply

Return type

None

pyspike.DiscreteFunc.average_profile(profiles)[source]

Computes the average profile from the given ISI- or SPIKE-profiles.

Parameters

profiles – list of PieceWiseConstFunc or PieceWiseLinFunc representing ISI- or SPIKE-profiles to be averaged.

Returns

the averages profile $$<S_{isi}>$$ or $$<S_{spike}>$$.

Return type

PieceWiseConstFunc or PieceWiseLinFunc

## Functions¶

### ISI-distance¶

pyspike.isi_distance.isi_distance(*args, **kwargs)[source]

Computes the ISI-distance $$D_I$$ of the given spike trains. The isi-distance is the integral over the isi distance profile $$I(t)$$:

$D_I = \int_{T_0}^{T_1} I(t) dt.$

In the multivariate case it is the integral over the multivariate ISI-profile, i.e. the average profile over all spike train pairs:

$D_I = \int_0^T \frac{2}{N(N-1)} \sum_{<i,j>} I^{i,j},$

where the sum goes over all pairs <i,j>

Valid call structures:

isi_distance(st1, st2)  # returns the bi-variate distance
isi_distance(st1, st2, st3)  # multi-variate distance of 3 spike trains

spike_trains = [st1, st2, st3, st4]  # list of spike trains
isi_distance(spike_trains)  # distance of the list of spike trains
isi_distance(spike_trains, indices=[0, 1])  # use only the spike trains
# given by the indices

Returns

The isi-distance $$D_I$$.

Return type

double

pyspike.isi_distance.isi_distance_bi(spike_train1, spike_train2, interval=None)[source]

Specific function to compute the bivariate ISI-distance. This is a deprecated function and should not be called directly. Use isi_distance() to compute ISI-distances.

Parameters
• spike_train1 (SpikeTrain) – First spike train.

• spike_train2 (SpikeTrain) – Second spike train.

• interval (Pair of floats or None.) – averaging interval given as a pair of floats (T0, T1), if None the average over the whole function is computed.

Returns

The isi-distance $$D_I$$.

Return type

double

pyspike.isi_distance.isi_distance_matrix(spike_trains, indices=None, interval=None)[source]

Computes the time averaged isi-distance of all pairs of spike-trains.

Parameters
• spike_trains – list of SpikeTrain

• indices (list or None) – list of indices defining which spike trains to use, if None all given spike trains are used (default=None)

• interval (Pair of floats or None.) – averaging interval given as a pair of floats, if None the average over the whole function is computed.

Returns

2D array with the pair wise time average isi distances $$D_{I}^{ij}$$

Return type

np.array

pyspike.isi_distance.isi_distance_multi(spike_trains, indices=None, interval=None)[source]

Specific function to compute the multivariate ISI-distance. This is a deprecfated function and should not be called directly. Use isi_distance() to compute ISI-distances.

Parameters
• spike_trains – list of SpikeTrain

• indices – list of indices defining which spike trains to use, if None all given spike trains are used (default=None)

• interval (Pair of floats or None.) – averaging interval given as a pair of floats, if None the average over the whole function is computed.

Returns

The time-averaged multivariate ISI distance $$D_I$$

Return type

double

pyspike.isi_distance.isi_profile(*args, **kwargs)[source]

Computes the isi-distance profile $$I(t)$$ of the given spike trains. Returns the profile as a PieceWiseConstFunc object. The ISI-values are defined positive $$I(t)>=0$$.

Valid call structures:

isi_profile(st1, st2)       # returns the bi-variate profile
isi_profile(st1, st2, st3)  # multi-variate profile of 3 spike trains

spike_trains = [st1, st2, st3, st4]  # list of spike trains
isi_profile(spike_trains)   # profile of the list of spike trains
isi_profile(spike_trains, indices=[0, 1])  # use only the spike trains
# given by the indices


The multivariate ISI distance profile for a set of spike trains is defined as the average ISI-profile of all pairs of spike-trains:

$<I(t)> = \frac{2}{N(N-1)} \sum_{<i,j>} I^{i,j},$

where the sum goes over all pairs <i,j>

Returns

The isi-distance profile $$I(t)$$

Return type

PieceWiseConstFunc

pyspike.isi_distance.isi_profile_bi(spike_train1, spike_train2)[source]

Specific function to compute a bivariate ISI-profile. This is a deprecated function and should not be called directly. Use isi_profile() to compute ISI-profiles.

Parameters
Returns

The isi-distance profile $$I(t)$$

Return type

PieceWiseConstFunc

pyspike.isi_distance.isi_profile_multi(spike_trains, indices=None)[source]

Specific function to compute the multivariate ISI-profile for a set of spike trains. This is a deprecated function and should not be called directly. Use isi_profile() to compute ISI-profiles.

Parameters
• spike_trains – list of SpikeTrain

• indices – list of indices defining which spike trains to use, if None all given spike trains are used (default=None)

Returns

The averaged isi profile $$<I(t)>$$

Return type

PieceWiseConstFunc

### SPIKE-distance¶

pyspike.spike_distance.spike_distance(*args, **kwargs)[source]

Computes the SPIKE-distance $$D_S$$ of the given spike trains. The spike-distance is the integral over the spike distance profile $$D(t)$$:

$D_S = \int_{T_0}^{T_1} S(t) dt.$

Valid call structures:

spike_distance(st1, st2)  # returns the bi-variate distance
spike_distance(st1, st2, st3)  # multi-variate distance of 3 spike trains

spike_trains = [st1, st2, st3, st4]  # list of spike trains
spike_distance(spike_trains)  # distance of the list of spike trains
spike_distance(spike_trains, indices=[0, 1])  # use only the spike trains
# given by the indices


In the multivariate case, the spike distance is given as the integral over the multivariate profile, that is the average profile of all spike train pairs:

$D_S = \int_0^T \frac{2}{N(N-1)} \sum_{<i,j>} S^{i, j} dt$
Returns

The spike-distance $$D_S$$.

Return type

double

pyspike.spike_distance.spike_distance_bi(spike_train1, spike_train2, interval=None)[source]

Specific function to compute a bivariate SPIKE-distance. This is a deprecated function and should not be called directly. Use spike_distance() to compute SPIKE-distances.

Parameters
• spike_train1 (SpikeTrain) – First spike train.

• spike_train2 (SpikeTrain) – Second spike train.

• interval (Pair of floats or None.) – averaging interval given as a pair of floats (T0, T1), if None the average over the whole function is computed.

Returns

The spike-distance.

Return type

double

pyspike.spike_distance.spike_distance_matrix(spike_trains, indices=None, interval=None)[source]

Computes the time averaged spike-distance of all pairs of spike-trains.

Parameters
• spike_trains – list of SpikeTrain

• indices (list or None) – list of indices defining which spike trains to use, if None all given spike trains are used (default=None)

• interval (Pair of floats or None.) – averaging interval given as a pair of floats, if None the average over the whole function is computed.

Returns

2D array with the pair wise time average spike distances $$D_S^{ij}$$

Return type

np.array

pyspike.spike_distance.spike_distance_multi(spike_trains, indices=None, interval=None)[source]

Specific function to compute a multivariate SPIKE-distance. This is a deprecated function and should not be called directly. Use spike_distance() to compute SPIKE-distances.

Parameters
• spike_trains – list of SpikeTrain

• indices (list or None) – list of indices defining which spike trains to use, if None all given spike trains are used (default=None)

• interval (Pair of floats or None.) – averaging interval given as a pair of floats, if None the average over the whole function is computed.

Returns

The averaged multi-variate spike distance $$D_S$$.

Return type

double

pyspike.spike_distance.spike_profile(*args, **kwargs)[source]

Computes the spike-distance profile $$S(t)$$ of the given spike trains. Returns the profile as a PieceWiseConstLin object. The SPIKE-values are defined positive $$S(t)>=0$$.

Valid call structures:

spike_profile(st1, st2)  # returns the bi-variate profile
spike_profile(st1, st2, st3)  # multi-variate profile of 3 spike trains

spike_trains = [st1, st2, st3, st4]  # list of spike trains
spike_profile(spike_trains)  # profile of the list of spike trains
spike_profile(spike_trains, indices=[0, 1])  # use only the spike trains
# given by the indices


The multivariate spike-distance profile is defined as the average of all pairs of spike-trains:

$<S(t)> = \frac{2}{N(N-1)} \sum_{<i,j>} S^{i, j},$

where the sum goes over all pairs <i,j>

Returns

The spike-distance profile $$S(t)$$

Return type

PieceWiseConstLin

pyspike.spike_distance.spike_profile_bi(spike_train1, spike_train2)[source]

Specific function to compute a bivariate SPIKE-profile. This is a deprecated function and should not be called directly. Use spike_profile() to compute SPIKE-profiles.

Parameters
Returns

The spike-distance profile $$S(t)$$.

Return type

PieceWiseLinFunc

pyspike.spike_distance.spike_profile_multi(spike_trains, indices=None)[source]

Specific function to compute a multivariate SPIKE-profile. This is a deprecated function and should not be called directly. Use spike_profile() to compute SPIKE-profiles.

Parameters
• spike_trains – list of SpikeTrain

• indices (list or None) – list of indices defining which spike trains to use, if None all given spike trains are used (default=None)

Returns

The averaged spike profile $$<S>(t)$$

Return type

PieceWiseLinFunc

### SPIKE-synchronization¶

pyspike.spike_sync.filter_by_spike_sync(spike_trains, threshold, indices=None, max_tau=None, return_removed_spikes=False)[source]

Removes the spikes with a multi-variate spike_sync value below threshold.

pyspike.spike_sync.spike_sync(*args, **kwargs)[source]

Computes the spike synchronization value SYNC of the given spike trains. The spike synchronization value is the computed as the total number of coincidences divided by the total number of spikes:

$SYNC = \sum_n C_n / N.$

Valid call structures:

spike_sync(st1, st2)  # returns the bi-variate spike synchronization
spike_sync(st1, st2, st3)  # multi-variate result for 3 spike trains

spike_trains = [st1, st2, st3, st4]  # list of spike trains
spike_sync(spike_trains)  # spike-sync of the list of spike trains
spike_sync(spike_trains, indices=[0, 1])  # use only the spike trains
# given by the indices


The multivariate SPIKE-Sync is again defined as the overall ratio of all coincidence values divided by the total number of spikes.

Returns

The spike synchronization value.

Return type

double

pyspike.spike_sync.spike_sync_bi(spike_train1, spike_train2, interval=None, max_tau=None)[source]

Specific function to compute a bivariate SPIKE-Sync value. This is a deprecated function and should not be called directly. Use spike_sync() to compute SPIKE-Sync values.

Parameters
• spike_train1 (pyspike.SpikeTrain) – First spike train.

• spike_train2 (pyspike.SpikeTrain) – Second spike train.

• interval (Pair of floats or None.) – averaging interval given as a pair of floats (T0, T1), if None the average over the whole function is computed.

• max_tau – Maximum coincidence window size. If 0 or None, the coincidence window has no upper bound.

Returns

The spike synchronization value.

Return type

double

pyspike.spike_sync.spike_sync_matrix(spike_trains, indices=None, interval=None, max_tau=None)[source]

Computes the overall spike-synchronization value of all pairs of spike-trains.

Parameters
• spike_trains – list of pyspike.SpikeTrain

• indices (list or None) – list of indices defining which spike trains to use, if None all given spike trains are used (default=None)

• interval (Pair of floats or None.) – averaging interval given as a pair of floats, if None the average over the whole function is computed.

• max_tau – Maximum coincidence window size. If 0 or None, the coincidence window has no upper bound.

Returns

2D array with the pair wise time spike synchronization values $$SYNC_{ij}$$

Return type

np.array

pyspike.spike_sync.spike_sync_multi(spike_trains, indices=None, interval=None, max_tau=None)[source]

Specific function to compute a multivariate SPIKE-Sync value. This is a deprecated function and should not be called directly. Use spike_sync() to compute SPIKE-Sync values.

Parameters
• spike_trains – list of pyspike.SpikeTrain

• indices (list or None) – list of indices defining which spike trains to use, if None all given spike trains are used (default=None)

• interval (Pair of floats or None.) – averaging interval given as a pair of floats, if None the average over the whole function is computed.

• max_tau – Maximum coincidence window size. If 0 or None, the coincidence window has no upper bound.

Returns

The multi-variate spike synchronization value SYNC.

Return type

double

pyspike.spike_sync.spike_sync_profile(*args, **kwargs)[source]

Computes the spike-synchronization profile S_sync(t) of the given spike trains. Returns the profile as a DiscreteFunction object. In the bivariate case, he S_sync values are either 1 or 0, indicating the presence or absence of a coincidence. For multi-variate cases, each spike in the set of spike trains, the profile is defined as the number of coincidences divided by the number of spike trains pairs involving the spike train of containing this spike, which is the number of spike trains minus one (N-1).

Valid call structures:

spike_sync_profile(st1, st2)  # returns the bi-variate profile
spike_sync_profile(st1, st2, st3)  # multi-variate profile of 3 sts

sts = [st1, st2, st3, st4]  # list of spike trains
spike_sync_profile(sts)  # profile of the list of spike trains
spike_sync_profile(sts, indices=[0, 1])  # use only the spike trains
# given by the indices


In the multivariate case, the profile is defined as the number of coincidences for each spike in the set of spike trains divided by the number of spike trains pairs involving the spike train of containing this spike, which is the number of spike trains minus one (N-1).

Returns

The spike-sync profile $$S_{sync}(t)$$.

Return type

pyspike.function.DiscreteFunction

pyspike.spike_sync.spike_sync_profile_bi(spike_train1, spike_train2, max_tau=None)[source]

Specific function to compute a bivariate SPIKE-Sync-profile. This is a deprecated function and should not be called directly. Use spike_sync_profile() to compute SPIKE-Sync-profiles.

Parameters
Returns

The spike-sync profile $$S_{sync}(t)$$.

Return type

pyspike.function.DiscreteFunction

pyspike.spike_sync.spike_sync_profile_multi(spike_trains, indices=None, max_tau=None)[source]

Specific function to compute a multivariate SPIKE-Sync-profile. This is a deprecated function and should not be called directly. Use spike_sync_profile() to compute SPIKE-Sync-profiles.

Parameters
• spike_trains – list of pyspike.SpikeTrain

• indices (list or None) – list of indices defining which spike trains to use, if None all given spike trains are used (default=None)

• max_tau – Maximum coincidence window size. If 0 or None, the coincidence window has no upper bound.

Returns

The multi-variate spike sync profile $$<S_{sync}>(t)$$

Return type

pyspike.function.DiscreteFunction

### PSTH¶

pyspike.psth.psth(spike_trains, bin_size)[source]

Computes the peri-stimulus time histogram of a set of SpikeTrain. The PSTH is simply the histogram of merged spike events. The bin_size defines the width of the histogram bins.

Parameters
Returns

The PSTH as a PieceWiseConstFunc

### Directionality¶

pyspike.spike_directionality.optimal_spike_train_sorting(spike_trains, indices=None, interval=None, max_tau=None, full_output=False)[source]

Finds the best sorting of the given spike trains by computing the spike directionality matrix and optimize the order using simulated annealing. For a detailed description of the algorithm see: http://iopscience.iop.org/article/10.1088/1367-2630/aa68c3/meta

Parameters
• spike_trains – list of SpikeTrain

• indices (list or None) – list of indices defining which spike trains to use, if None all given spike trains are used (default=None)

• interval (Pair of floats or None.) – time interval filter given as a pair of floats, if None the full spike trains are used (default=None).

• max_tau – Maximum coincidence window size. If 0 or None, the coincidence window has no upper bound (default=None).

• full_output – If true, then function will additionally return the number of performed iterations (default=False)

Returns

(p, F) - tuple with the optimal permutation and synfire indicator. if full_output=True , (p, F, iter) is returned.

pyspike.spike_directionality.permutate_matrix(D, p)[source]

Helper function that applies the permutation p to the columns and rows of matrix D. Return the permutated matrix $$D'[n,m] = D[p[n], p[m]]$$.

Parameters
• D – The matrix.

• d – The permutation.

Returns

The permuated matrix D’, ie $$D'[n,m] = D[p[n], p[m]]$$

pyspike.spike_directionality.spike_directionality(spike_train1, spike_train2, normalize=True, interval=None, max_tau=None)[source]

Computes the overall spike directionality of the first spike train with respect to the second spike train.

Parameters
Returns

The spike train order profile $$E(t)$$.

pyspike.spike_directionality.spike_directionality_matrix(spike_trains, normalize=True, indices=None, interval=None, max_tau=None)[source]

Computes the spike directionality matrix for the given spike trains.

Parameters
• spike_trains (List of pyspike.SpikeTrain) – List of spike trains.

• normalize – Normalize by the number of spikes (multiplicity).

• indices (list or None) – list of indices defining which spike trains to use, if None all given spike trains are used (default=None)

• max_tau – Maximum coincidence window size. If 0 or None, the coincidence window has no upper bound.

Returns

The spike-directionality values.

pyspike.spike_directionality.spike_directionality_values(*args, **kwargs)[source]

Computes the spike directionality value for each spike in each spike train. Returns a list containing an array of spike directionality values for every given spike train.

Valid call structures:

spike_directionality_values(st1, st2)       # returns the bi-variate profile
spike_directionality_values(st1, st2, st3)  # multi-variate profile of 3
# spike trains

spike_trains = [st1, st2, st3, st4]          # list of spike trains
spike_directionality_values(spike_trains)    # profile of the list of spike trains
spike_directionality_values(spike_trains, indices=[0, 1])  # use only the spike trains
# given by the indices


Additonal arguments: :param max_tau: Upper bound for coincidence window (default=None). :param indices: list of indices defining which spike trains to use,

if None all given spike trains are used (default=None)

Returns

The spike directionality values $$D^n_i$$ as a list of arrays.

pyspike.spike_directionality.spike_train_order(*args, **kwargs)[source]

Computes the spike train order (Synfire Indicator) of the given spike trains.

Valid call structures:

spike_train_order(st1, st2, normalize=True)  # normalized bi-variate
# spike train order
spike_train_order(st1, st2, st3)  # multi-variate result of 3 spike trains

spike_trains = [st1, st2, st3, st4]       # list of spike trains
spike_train_order(spike_trains)   # result for the list of spike trains
spike_train_order(spike_trains, indices=[0, 1])  # use only the spike trains
# given by the indices

• max_tau Upper bound for coincidence window, default=None.

• normalize Flag indicating if the reslut should be normalized by the number of spikes , default=False

Returns

The spike train order value (Synfire Indicator)

pyspike.spike_directionality.spike_train_order_bi(spike_train1, spike_train2, normalize=True, interval=None, max_tau=None)[source]

Computes the overall spike train order value (Synfire Indicator) for two spike trains.

Parameters
Returns

The spike train order value (Synfire Indicator)

pyspike.spike_directionality.spike_train_order_multi(spike_trains, indices=None, normalize=True, interval=None, max_tau=None)[source]

Computes the overall spike train order value (Synfire Indicator) for many spike trains.

Parameters
• spike_trains – list of SpikeTrain

• indices – list of indices defining which spike trains to use, if None all given spike trains are used (default=None)

• normalize – Normalize by the number of spike (multiplicity).

• interval (Pair of floats or None.) – averaging interval given as a pair of floats, if None the average over the whole function is computed.

• max_tau – Maximum coincidence window size. If 0 or None, the coincidence window has no upper bound.

Returns

Spike train order values (Synfire Indicator) F for the given spike trains.

Return type

double

pyspike.spike_directionality.spike_train_order_profile(*args, **kwargs)[source]

Computes the spike train order profile $$E(t)$$ of the given spike trains. Returns the profile as a DiscreteFunction object.

Valid call structures:

spike_train_order_profile(st1, st2)       # returns the bi-variate profile
spike_train_order_profile(st1, st2, st3)  # multi-variate profile of 3
# spike trains

spike_trains = [st1, st2, st3, st4]       # list of spike trains
spike_train_order_profile(spike_trains)   # profile of the list of spike trains
spike_train_order_profile(spike_trains, indices=[0, 1])  # use only the spike trains
# given by the indices


Additonal arguments: :param max_tau: Upper bound for coincidence window, default=None. :param indices: list of indices defining which spike trains to use,

if None all given spike trains are used (default=None)

Returns

The spike train order profile $$E(t)$$

Return type

DiscreteFunction

pyspike.spike_directionality.spike_train_order_profile_bi(spike_train1, spike_train2, max_tau=None)[source]

Computes the spike train order profile P(t) of the two given spike trains. Returns the profile as a DiscreteFunction object.

Parameters
Returns

The spike train order profile $$E(t)$$.

Return type

pyspike.function.DiscreteFunction

pyspike.spike_directionality.spike_train_order_profile_multi(spike_trains, indices=None, max_tau=None)[source]

Computes the multi-variate spike train order profile for a set of spike trains. For each spike in the set of spike trains, the multi-variate profile is defined as the sum of asymmetry values divided by the number of spike trains pairs involving the spike train of containing this spike, which is the number of spike trains minus one (N-1).

Parameters
• spike_trains – list of pyspike.SpikeTrain

• indices (list or None) – list of indices defining which spike trains to use, if None all given spike trains are used (default=None)

• max_tau – Maximum coincidence window size. If 0 or None, the coincidence window has no upper bound.

Returns

The multi-variate spike sync profile $$<S_{sync}>(t)$$

Return type

pyspike.function.DiscreteFunction

### Helper functions¶

pyspike.spikes.generate_poisson_spikes(rate, interval)[source]

Generates a Poisson spike train with the given rate in the given time interval

Parameters
• rate – The rate of the spike trains

• interval (pair of doubles or double) – A pair (T_start, T_end) of values representing the start and end time of the spike train measurement or a single value representing the end time, the T_start is then assuemd as 0. Auxiliary spikes will be added to the spike train at the beginning and end of this interval, if they are not yet present.

Returns

Poisson spike train as a SpikeTrain

pyspike.spikes.import_spike_trains_from_time_series(file_name, start_time, time_bin, separator=None, comment='#')[source]

Imports spike trains from time series consisting of 0 and 1 denoting the absence or presence of a spike. Each line in the data file represents one spike train.

Parameters
• file_name – The name of the data file containing the time series.

• edges – A pair (T_start, T_end) of values representing the start and end time of the spike train measurement or a single value representing the end time, the T_start is then assuemd as 0.

• separator – The character used to seprate the values in the text file

• comment – Lines starting with this character are ignored.

pyspike.spikes.load_spike_trains_from_txt(file_name, edges, separator=' ', comment='#', is_sorted=False, ignore_empty_lines=True)[source]

Loads a number of spike trains from a text file. Each line of the text file should contain one spike train as a sequence of spike times separated by separator. Empty lines as well as lines starting with comment are neglected. The edges represents the start and the end of the spike trains.

Parameters
• file_name – The name of the text file.

• edges – A pair (T_start, T_end) of values representing the start and end time of the spike train measurement or a single value representing the end time, the T_start is then assuemd as 0.

• separator – The character used to seprate the values in the text file

• comment – Lines starting with this character are ignored.

• sort – If true, the spike times are order via np.sort, default=True

Returns

list of SpikeTrain

pyspike.spikes.merge_spike_trains(spike_trains)[source]

Merges a number of spike trains into a single spike train.

Parameters

spike_trains – list of SpikeTrain

Returns

spike train with the merged spike times

pyspike.spikes.save_spike_trains_to_txt(spike_trains, file_name, separator=' ', precision=8)[source]

Saves the given spike trains into a file with the given file name. Each spike train will be stored in one line in the text file with the times separated by separator.

Parameters
pyspike.spikes.spike_train_from_string(s, edges, sep=' ', is_sorted=False)[source]

Converts a string of times into a SpikeTrain.

Parameters
• s – the string with (ordered) spike times.

• edges – interval defining the edges of the spike train. Given as a pair of floats (T0, T1) or a single float T1, where T0=0 is assumed.

• sep – The separator between the time numbers, default=’ ‘.

• is_sorted – if True, the spike times are not sorted after loading, if False, spike times are sorted with np.sort

Returns

SpikeTrain`