"""
.. autofunction:: binned_spike_trains(trains, bin_size, start=0 ms, stop=None)
.. autofunction:: psth(trains, bin_size, rate_correction=True, start=0 ms, stop=None)
.. autofunction:: spike_density_estimation(trains, start=0 ms, stop=None, evaluation_points=None, kernel=gauss_kernel, kernel_size=100 ms, optimize_steps=None, progress=None)
"""
from __future__ import division
import scipy as sp
import quantities as pq
import neo
from progress_indicator import ProgressIndicator
from . import SpykeException
def _binned_spike_trains(trains, bins):
""" Return a binned representation of SpikeTrain objects.
:param sequencs trains: A sequence of SpikeTrain objects.
:param bins: The bin edges, including the rightmost edge.
:type bins: Quantity 1D
:returns: List of one-dimensional arrays of spike counts.
:rtype: list
"""
counts = []
for t in trains:
counts.append(sp.histogram(t.rescale(bins.units), bins)[0])
return counts
[docs]def binned_spike_trains(trains, bin_size, start=0*pq.ms, stop=None):
""" Return dictionary of binned rates for a dictionary of
SpikeTrain lists.
:param dict trains: A sequence of `SpikeTrain` lists.
:param bin_size: The desired bin size (as a time quantity).
:type bin_size: Quantity scalar
:type start: The desired time for the start of the first bin.
It will be recalculated if there are spike trains which
start later than this time.
:type start: Quantity scalar
:param stop: The desired time for the end of the last bin. It will
be recalculated if there are spike trains which end earlier
than this time.
:type stop: Quantity scalar
:returns: A dictionary (with the same indices as ``trains``) of lists
of spike train counts and the bin borders.
:rtype: dict, Quantity 1D
"""
# Do not create bins that do not include all spike trains
max_start, max_stop = minimum_spike_train_interval(trains)
start = max(start, max_start)
start.units = bin_size.units
if stop is not None:
stop = min(stop, max_stop)
else:
stop = max_stop
stop.units = bin_size.units
# Calculate bin size
bins = sp.arange(start, stop, bin_size)*bin_size.units
# Create dictionary for all SpikeTrain lists
binned = {}
for s in trains:
b = _binned_spike_trains(trains[s], bins)
if b:
binned[s] = b
return binned, bins
[docs]def psth(trains, bin_size, rate_correction=True, start=0*pq.ms, stop=None):
""" Return dictionary of peri stimulus time histograms for a dictionary
of SpikeTrain lists.
:param dict trains: A dictionary of lists of SpikeTrain objects.
:param bin_size: The desired bin size (as a time quantity).
:type bin_size: Quantity scalar
:param bool rate_correction: Determines if a rates (``True``) or
counts (``False``) are returned.
:param start: The desired time for the start of the first bin. It
will be recalculated if there are spike trains which start
later than this time.
:type start: Quantity scalar
:param stop: The desired time for the end of the last bin. It will
be recalculated if there are spike trains which end earlier
than this time.
:type stop: Quantity scalar
:returns: A dictionary (with the same indices as ``trains``) of arrays
containing counts (or rates if ``rate_correction`` is ``True``)
and the bin borders.
:rtype: dict, Quantity 1D
"""
if not trains:
raise SpykeException('No spike trains for PSTH!')
binned, bins = binned_spike_trains(trains, bin_size, start, stop)
cumulative = {}
time_multiplier = 1.0 / float(bin_size.rescale(pq.s))
for u in binned:
if rate_correction:
cumulative[u] = sp.mean(sp.array(binned[u]), 0)
else:
cumulative[u] = sp.sum(sp.array(binned[u]), 0)
cumulative[u] *= time_multiplier
return cumulative, bins
[docs]def aligned_spike_trains(trains, events, copy=True):
""" Return a list of spike trains aligned to an event (the event will
be time 0 on the returned trains).
:param dict trains: A list of SpikeTrain objects.
:param dict events: A dictionary of Event objects, indexed by segment.
These events (in case of lists, always the first element in the list)
will be used to align the spike trains and will be at time 0 for
the aligned spike trains.
:param bool copy: Determines if aligned copies of the original
spike trains will be returned. If not, every spike train needs
exactly one corresponding event, otherwise a ``ValueError`` will
be raised. Otherwise, entries with no event will be ignored.
"""
ret = []
for t in trains:
s = t.segment
if s not in events:
if not copy:
raise ValueError(
'Cannot align spike trains: At least one segment does' +
'not have an align event.')
continue
if copy:
st = t.rescale(t.units)
else:
st = t
e = events[s]
st -= e.time
st.t_stop -= e.time
st.t_start -= e.time
ret.append(st)
return ret
[docs]def minimum_spike_train_interval(trains):
""" Computes the minimum starting time and maximum end time that all
given spike trains share.
:param dict trains: A dictionary of sequences of SpikeTrain
objects.
:returns: Maximum shared start time and minimum shared stop time.
:rtype: Quantity scalar, Quantity scalar
"""
# Hoping that nobody needs a 1000 year long spike train
start = -1000 * pq.year
stop = 1000 * pq.year
# Load data and find shortest spike train
for st in trains.itervalues():
# Minimum length of spike of all spike trains for this unit
start = max(start, max((t.t_start for t in st)))
stop = min(stop, min((t.t_stop for t in st)))
return start, stop
def gauss_kernel(x, kernel_size):
return 1.0 / (sp.sqrt(2*sp.pi) * kernel_size) * \
sp.exp(-x**2 / (2 * kernel_size)**2)
[docs]def spike_density_estimation(trains, start=0*pq.ms, stop=None,
evaluation_points=None, kernel=gauss_kernel,
kernel_size=100*pq.ms, optimize_steps=None,
progress=None):
""" Create a spike density estimation from a dictionary of
lists of SpikeTrain objects. The spike density estimations give
an estimate of the instantaneous rate. Optionally finds optimal
kernel size for given data.
:param dict trains: A dictionary of SpikeTrain lists.
:param start: The desired time for the start of the first bin. It
will be recalculated if there are spike trains which start later
than this time. This parameter can be negative (which could be
useful when aligning on events).
:type start: Quantity scalar
:param stop: The desired time for the end of the last bin. It will
be recalculated if there are spike trains which end earlier
than this time.
:type stop: Quantity scalar
:param evaluation_points: An array of time points at which the
density estimation is evaluated to produce the data. If this
is None, 1000 equally spaced points covering the range of the
input spike trains will be used.
:type evaluation_points: Quantity 1D
:param func kernel: The kernel function to use, should accept
two parameters: A ndarray of distances and a kernel size.
The total area under the kernel function sould be 1.
Default: Gaussian kernel
:param kernel_size: A uniform kernel size for all spike trains.
Only used if optimization of kernel sizes is not used.
:type kernel_size: Quantity scalar
:param optimize_steps: An array of time lengths that will be
considered in the kernel width optimization. Note that the
optimization assumes a Gaussian kernel and will most likely
not give the optimal kernel size if another kernel is used.
If None, ``kernel_size`` will be used.
:type optimize_steps: Quantity 1D
:param progress: Set this parameter to report progress.
:type progress: :class:`spykeutils.progress_indicator.ProgressIndicator`
:returns: Three values:
* A dictionary of the spike density estimations (Quantity 1D in
Hz). Indexed the same as ``trains``.
* A dictionary of kernel sizes (Quantity scalars). Indexed the
same as ``trains``.
* The used evaluation points.
:rtype: dict, dict, Quantity 1D
"""
if not progress:
progress = ProgressIndicator()
if optimize_steps is None or len(optimize_steps) < 1:
units = kernel_size.units
kernel_size = {u:kernel_size for u in trains}
else:
# Find optimal kernel size for all spike train sets
progress.set_ticks(len(optimize_steps)*len(trains))
progress.set_status('Calculating optimal kernel size')
units = optimize_steps.units
kernel_size = {}
for u,t in trains.iteritems():
c = collapsed_spike_trains(t)
kernel_size[u] = optimal_gauss_kernel_size(c, optimize_steps,
progress)
# Prepare evaluation points
if evaluation_points is None:
max_start, max_stop = minimum_spike_train_interval(trains)
start = max(start, max_start)
start.units = units
if stop is not None:
stop = min(stop, max_stop)
else:
stop = max_stop
stop.units = units
evaluation_points = sp.linspace(start, stop, 1000)
progress.set_ticks(len(trains) * len(evaluation_points))
progress.set_status('Creating spike density plot')
# Calculate KDEs
kde = {}
for u,t in trains.iteritems():
this_kde = []
# Collapse spike trains
collapsed = sp.asarray(collapsed_spike_trains(t).rescale(units))
ksize = float(kernel_size[u])
# Create density estimation
for p in evaluation_points:
dist = collapsed - float(p)
this_kde.append(sum(kernel(dist, ksize)))
progress.step()
kde[u] = sp.asarray(this_kde) / len(trains[u]) / units
kde[u].units = pq.Hz
return kde, kernel_size, evaluation_points
[docs]def collapsed_spike_trains(trains):
""" Return a superposition of a list of spike trains.
:param iterable trains: A list of SpikeTrain objects
:returns: A SpikeTrain object containing all spikes of the given
SpikeTrain objects.
"""
if not trains:
return neo.SpikeTrain([], 0)
start = min((t.t_start for t in trains))
stop = max((t.t_stop for t in trains))
collapsed = []
for t in trains:
collapsed.extend(sp.asarray(t.rescale(stop.units)))
return neo.SpikeTrain(collapsed*stop.units, t_stop=stop, t_start=start)
[docs]def optimal_gauss_kernel_size(train, optimize_steps, progress=None):
""" Return the optimal kernel size for a spike density estimation
of a SpikeTrain for a gaussian kernel. This function takes a single
spike train, which can be a superposition of multiple spike trains
(created with :func:`collapsed_spike_trains`) that should be included
in a spike density estimation.
See (Shimazaki, Shinomoto. Journal of Computational Neuroscience. 2010).
:param SpikeTrain train: The spike train for which the kernel
size should be optimized.
:param optimize_steps: Array of kernel sizes to try (the best of
these sizes will be returned).
:type optimize_steps: Quantity 1D
:param progress: Set this parameter to report progress. Will be
advanced by len(`optimize_steps`) steps.
:type progress: :class:`spykeutils.progress_indicator.ProgressIndicator`
:returns: Best of the given kernel sizes
:rtype: Quantity scalar
"""
if not progress:
progress = ProgressIndicator()
x = sp.asarray(train.rescale(optimize_steps.units))
steps = sp.asarray(optimize_steps)
N = len(train)
tau = sp.triu(sp.vstack([x] * N) - sp.vstack([x] * N).T, 1)
idx = sp.triu(sp.ones((N,N)), 1)
TAU = tau.T[idx.T==1]**2
C = {}
for s in steps:
C[s] = N/s + 1/s * sum(2 * sp.exp(-TAU/(4 * s**2)) -
4 * sp.sqrt(2) * sp.exp(-TAU/(2 * s**2)))
progress.step()
# Return kernel size with smallest cost
return min(C, key=C.get)*train.units