# Source code for elephant.spike_train_synchrony

```# -*- coding: utf-8 -*-
"""
Functions to measure the synchrony of several spike trains.

Synchrony Measures
------------------

.. autosummary::
:toctree: _toctree/spike_train_synchrony/

spike_contrast
Synchrotool

"""
from __future__ import division, print_function, unicode_literals

import warnings
from collections import namedtuple
from copy import deepcopy

import neo
import numpy as np
import quantities as pq

from elephant.statistics import Complexity
from elephant.utils import is_time_quantity, check_same_units

SpikeContrastTrace = namedtuple("SpikeContrastTrace", (
"contrast", "active_spiketrains", "synchrony", "bin_size"))

__all__ = [
"SpikeContrastTrace",
"spike_contrast",
"Synchrotool"
]

def _get_theta_and_n_per_bin(spiketrains, t_start, t_stop, bin_size):
"""
Calculates theta (amount of spikes per bin) and the amount of active spike
trains per bin of one spike train.
"""
bin_step = bin_size / 2
edges = np.arange(t_start, t_stop + bin_step, bin_step)
# Calculate histogram for every spike train
histogram = np.vstack([
_binning_half_overlap(st, edges=edges)
for st in spiketrains
])
# Amount of spikes per bin
theta = histogram.sum(axis=0)
# Amount of active spike trains per bin
n_active_per_bin = np.count_nonzero(histogram, axis=0)

return theta, n_active_per_bin

def _binning_half_overlap(spiketrain, edges):
"""
Referring to  overlapping the bins creates a better result.
"""
histogram, bin_edges = np.histogram(spiketrain, bins=edges)
histogram = histogram[:-1] + histogram[1:]
return histogram

[docs]def spike_contrast(spiketrains, t_start=None, t_stop=None,
min_bin=10 * pq.ms, bin_shrink_factor=0.9,
return_trace=False):
"""
Calculates the synchrony of spike trains, according to
:cite:`synchrony-Ciba18_136`. The spike trains can have different lengths.

Original implementation by: Philipp Steigerwald [s160857@th-ab.de]

Visualization is covered in
:func:`viziphant.spike_train_synchrony.plot_spike_contrast`.

Parameters
----------
spiketrains : list of neo.SpikeTrain
A list of input spike trains to calculate the synchrony from.
t_start : pq.Quantity, optional
The beginning of the spike train. If None, it's taken as the minimum
value of `t_start`s of the input spike trains.
Default: None
t_stop : pq.Quantity, optional
The end of the spike train. If None, it's taken as the maximum value
of `t_stop` of the input spike trains.
Default: None
min_bin : pq.Quantity, optional
Sets the minimum value for the `bin_min` that is calculated by the
algorithm and defines the smallest bin size to compute the histogram
of the input `spiketrains`.
Default: 0.01 ms
bin_shrink_factor : float, optional
A multiplier to shrink the bin size on each iteration. The value must
be in range `(0, 1)`.
Default: 0.9
return_trace : bool, optional
If set to True, returns a history of spike-contrast synchrony, computed
for a range of different bin sizes, alongside with the maximum value of
the synchrony.
Default: False

Returns
-------
synchrony : float
Returns the synchrony of the input spike trains.
spike_contrast_trace : namedtuple
If `return_trace` is set to True, a `SpikeContrastTrace` namedtuple is
returned with the following attributes:

`.contrast` - the average sum of differences of the number of spikes
in subsuequent bins;

`.active_spiketrains` - the average number of spikes per bin,
weighted by the number of spike trains containing at least one spike
inside the bin;

`.synchrony` - the product of `contrast` and `active_spiketrains`;

`.bin_size` - the X axis, a list of bin sizes that correspond to
these traces.

Raises
------
ValueError
If `bin_shrink_factor` is not in (0, 1) range.

If the input spike trains constist of a single spiketrain.

If all input spike trains contain no more than 1 spike.
TypeError
If the input spike trains is not a list of `neo.SpikeTrain` objects.

If `t_start`, `t_stop`, or `min_bin` are not time quantities.

Examples
--------
>>> import quantities as pq
>>> from elephant.spike_train_generation import homogeneous_poisson_process
>>> from elephant.spike_train_synchrony import spike_contrast
>>> spiketrain_1 = homogeneous_poisson_process(rate=20*pq.Hz,
...     t_stop=1000*pq.ms)
>>> spiketrain_2 = homogeneous_poisson_process(rate=20*pq.Hz,
...     t_stop=1000*pq.ms)
>>> spike_contrast([spiketrain_1, spiketrain_2])
0.4192546583850932

"""
if not 0. < bin_shrink_factor < 1.:
raise ValueError(f"'bin_shrink_factor' ({bin_shrink_factor}) must be "
"in range (0, 1).")
if not len(spiketrains) > 1:
raise ValueError("Spike contrast measure requires more than 1 input "
"spiketrain.")
check_same_units(spiketrains, object_type=neo.SpikeTrain)
if not is_time_quantity(t_start, t_stop, allow_none=True):
raise TypeError("'t_start' and 't_stop' must be time quantities.")
if not is_time_quantity(min_bin):
raise TypeError("'min_bin' must be a time quantity.")

if t_start is None:
t_start = min(st.t_start for st in spiketrains)
if t_stop is None:
t_stop = max(st.t_stop for st in spiketrains)

# convert everything to spiketrain units
units = spiketrains.units
spiketrains = [st.magnitude for st in spiketrains]
t_start = t_start.rescale(units).item()
t_stop = t_stop.rescale(units).item()
min_bin = min_bin.rescale(units).item()

spiketrains = [times[(times >= t_start) & (times <= t_stop)]
for times in spiketrains]

n_spiketrains = len(spiketrains)
n_spikes_total = sum(map(len, spiketrains))

duration = t_stop - t_start
bin_max = duration / 2

try:
isi_min = min(np.diff(st).min() for st in spiketrains if len(st) > 1)
except TypeError:
raise ValueError("All input spiketrains contain no more than 1 spike.")
bin_min = max(isi_min / 2, min_bin)

contrast_list = []
active_spiketrains = []
synchrony_curve = []

# Set new time boundaries
t_start = t_start - isi_min
t_stop = t_stop + isi_min

bin_sizes = []
bin_size = bin_max
while bin_size >= bin_min:
bin_sizes.append(bin_size)
# Calculate Theta and n
theta_k, n_k = _get_theta_and_n_per_bin(spiketrains,
t_start=t_start,
t_stop=t_stop,
bin_size=bin_size)

# calculate synchrony_curve = contrast * active_st
active_st = (np.sum(n_k * theta_k) / np.sum(theta_k) - 1) / (
n_spiketrains - 1)
contrast = np.sum(np.abs(np.diff(theta_k))) / (2 * n_spikes_total)
# Contrast: sum(|derivation|) / (2*#Spikes)
synchrony = contrast * active_st

contrast_list.append(contrast)
active_spiketrains.append(active_st)
synchrony_curve.append(synchrony)

# New bin size
bin_size *= bin_shrink_factor

# Sync value is maximum of the cost function C
synchrony = max(synchrony_curve)

if return_trace:
spike_contrast_trace = SpikeContrastTrace(
contrast=contrast_list,
active_spiketrains=active_spiketrains,
synchrony=synchrony_curve,
bin_size=bin_sizes * units,
)
return synchrony, spike_contrast_trace

return synchrony

[docs]class Synchrotool(Complexity):
"""
Tool class to find, remove and/or annotate the presence of synchronous
spiking events across multiple spike trains.

The complexity is used to characterize synchronous events within the same
spike train and across different spike trains in the `spiketrains` list.
This way synchronous events can be found both in multi-unit and
single-unit spike trains.

This class inherits from :class:`elephant.statistics.Complexity`, see its
documentation for more details and input parameters description.

--------
elephant.statistics.Complexity

"""

def __init__(self, spiketrains,
sampling_rate,
bin_size=None,
binary=True,
tolerance=1e-8):

self.annotated = False

super(Synchrotool, self).__init__(spiketrains=spiketrains,
bin_size=bin_size,
sampling_rate=sampling_rate,
binary=binary,
tolerance=tolerance)

[docs]    def delete_synchrofacts(self, threshold, in_place=False, mode='delete'):
"""
Delete or extract synchronous spiking events.

Parameters
----------
threshold : int
Threshold value for the deletion of spikes engaged in synchronous
activity.
* `deletion_threshold >= 2` leads to all spikes with a larger or
equal complexity value to be deleted/extracted.
* `deletion_threshold <= 1` leads to a ValueError, since this
would delete/extract all spikes and there are definitely more
efficient ways of doing so.
in_place : bool, optional
Determines whether the modification are made in place
on ``self.input_spiketrains``.
Default: False
mode : {'delete', 'extract'}, optional
Inversion of the mask for deletion of synchronous events.
* ``'delete'`` leads to the deletion of all spikes with
complexity >= `threshold`,
i.e. deletes synchronous spikes.
* ``'extract'`` leads to the deletion of all spikes with
complexity < `threshold`, i.e. extracts synchronous spikes.
Default: 'delete'

Raises
------
ValueError
If `mode` is not one in {'delete', 'extract'}.

If `threshold <= 1`.

Returns
-------
list of neo.SpikeTrain
List of spiketrains where the spikes with
``complexity >= threshold`` have been deleted/extracted.
* If ``in_place`` is True, the returned list is the same as
``self.input_spiketrains``.
* If ``in_place`` is False, the returned list is a deepcopy of
``self.input_spiketrains``.

"""

if not self.annotated:
self.annotate_synchrofacts()

if mode not in ['delete', 'extract']:
raise ValueError(f"Invalid mode '{mode}'. Valid modes are: "
f"'delete', 'extract'")

if threshold <= 1:
raise ValueError('A deletion threshold <= 1 would result '
'in the deletion of all spikes.')

if in_place:
spiketrain_list = self.input_spiketrains
else:
spiketrain_list = deepcopy(self.input_spiketrains)

for idx, st in enumerate(spiketrain_list):
if mode == 'extract':
if in_place and st.segment is not None:
segment = st.segment

try:
# replace link to spiketrain in segment
new_index = self._get_spiketrain_index(
segment.spiketrains, st)
# Todo: Simplify following lines once Neo SpikeTrainList
# implments indexed assignment of entries (i.e., stl[i]=st)
spiketrainlist = list(segment.spiketrains)
spiketrainlist[new_index] = new_st
segment.spiketrains = spiketrainlist
except ValueError:
# st is not in this segment even though it points to it
warnings.warn(f"The SpikeTrain at index {idx} of the "
"input list spiketrains has a "
"unidirectional uplink to a segment in "
"whose segment.spiketrains list it does not "
"appear. Only the spiketrains in the input "
"list will be replaced. You can suppress "
"this warning by setting "
"spiketrain.segment=None for the input "
"spiketrains.")

block = segment.block
if block is not None:
# replace link to spiketrain in groups
for group in block.groups:
try:
idx = self._get_spiketrain_index(
group.spiketrains,
st)
except ValueError:
# st is not in this group, move to next group
continue

# st found in group, replace with new_st
group.spiketrains[idx] = new_st
spiketrain_list[idx] = new_st

return spiketrain_list

[docs]    def annotate_synchrofacts(self):
"""
Annotate the complexity of each spike in the
``self.epoch.array_annotations`` *in-place*.
"""
epoch_complexities = self.epoch.array_annotations['complexity']
right_edges = (
self.epoch.times.magnitude.flatten()
+ self.epoch.durations.rescale(
self.epoch.times.units).magnitude.flatten()
)

for idx, st in enumerate(self.input_spiketrains):

# all indices of spikes that are within the half-open intervals
# defined by the boundaries
# note that every second entry in boundaries is an upper boundary
spike_to_epoch_idx = np.searchsorted(
right_edges,
st.times.rescale(self.epoch.times.units).magnitude.flatten())
complexity_per_spike = epoch_complexities[spike_to_epoch_idx]

st.array_annotate(complexity=complexity_per_spike)

self.annotated = True

def _get_spiketrain_index(self, spiketrain_list, spiketrain):
for index, item in enumerate(spiketrain_list):
if item is spiketrain:
return index