# Source code for spykeutils.rate_estimation

```
from __future__ import division
import scipy as sp
import quantities as pq
import neo
from progress_indicator import ProgressIndicator
import signal_processing as sigproc
import tools
import copy as cp
from . import SpykeException
[docs]def psth(
trains, bin_size, rate_correction=True, start=0 * pq.ms,
stop=sp.inf * pq.s):
""" Return dictionary of peri stimulus time histograms for a dictionary
of spike train lists.
:param dict trains: A dictionary of lists of :class:`neo.core.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!')
start, stop = tools.minimum_spike_train_interval(trains, start, stop)
binned, bins = tools.bin_spike_trains(trains, 1.0 / 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 list trains: A list of :class:`neo.core.SpikeTrain` objects.
:param dict events: A dictionary of Event objects, indexed by segment.
These events 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
e = events[s]
if copy:
st = neo.SpikeTrain(
t, t.t_stop, units=t.units,
sampling_rate=t.sampling_rate, t_start=t.t_start,
waveforms=t.waveforms, left_sweep=t.left_sweep,
name=t.name, file_origin=t.file_origin,
description=t.description, **t.annotations)
else:
st = t
st -= e.time
st.t_stop -= e.time
st.t_start -= e.time
ret.append(st)
return ret
[docs]def spike_density_estimation(trains, start=0 * pq.ms, stop=None,
kernel=None, kernel_size=100 * pq.ms,
optimize_steps=None, progress=None):
""" Create a spike density estimation from a dictionary of
lists of spike trains.
The spike density estimations give an estimate of the instantaneous
rate. The density estimation is evaluated at 1024 equally spaced
points covering the range of the input spike trains. Optionally finds
optimal kernel size for given data using the algorithm from
(Shimazaki, Shinomoto. Journal of Computational Neuroscience. 2010).
:param dict trains: A dictionary of :class:`neo.core.SpikeTrain` lists.
:param start: The desired time for the start of the estimation. 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 estimation. It will
be recalculated if there are spike trains which end earlier
than this time.
:type stop: Quantity scalar
:param kernel: The kernel function or instance to use, should accept
two parameters: A ndarray of distances and a kernel size.
The total area under the kernel function should be 1.
Automatic optimization assumes a Gaussian kernel and will
likely not produce optimal results for different kernels.
Default: Gaussian kernel
:type kernel: func or :class:`.signal_processing.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:`.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
else:
units = optimize_steps.units
if kernel is None:
kernel = sigproc.GaussianKernel(100 * pq.ms)
# Prepare evaluation points
max_start, max_stop = tools.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
bins = sp.linspace(start, stop, 1025)
eval_points = bins[:-1] + (bins[1] - bins[0]) / 2
if optimize_steps is None or len(optimize_steps) < 1:
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')
kernel_size = {}
for u, t in trains.iteritems():
c = collapsed_spike_trains(t)
kernel_size[u] = optimal_gauss_kernel_size(
c.time_slice(start, stop), optimize_steps, progress)
progress.set_ticks(len(trains))
progress.set_status('Creating spike density plot')
# Calculate KDEs
kde = {}
for u, t in trains.iteritems():
# Collapse spike trains
collapsed = collapsed_spike_trains(t).rescale(units)
scaled_kernel = sigproc.as_kernel_of_size(kernel, kernel_size[u])
# Create density estimation using convolution
sliced = collapsed.time_slice(start, stop)
sampling_rate = 1024.0 / (sliced.t_stop - sliced.t_start)
kde[u] = sigproc.st_convolve(
sliced, scaled_kernel, sampling_rate,
kernel_discretization_params={
'num_bins': 2048, 'ensure_unit_area': True})[0] / len(trains[u])
kde[u].units = pq.Hz
return kde, kernel_size, eval_points
[docs]def collapsed_spike_trains(trains):
""" Return a superposition of a list of spike trains.
:param iterable trains: A list of :class:`neo.core.SpikeTrain` objects
:returns: A spike train object containing all spikes of the given
spike trains.
:rtype: :class:`neo.core.SpikeTrain`
"""
if not trains:
return neo.SpikeTrain([], 0 * pq.s)
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 spike train 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.
Implements the algorithm from
(Shimazaki, Shinomoto. Journal of Computational Neuroscience. 2010).
:param train: The spike train for which the kernel
size should be optimized.
:type train: :class:`neo.core.SpikeTrain`
: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:`.progress_indicator.ProgressIndicator`
:returns: Best of the given kernel sizes
:rtype: Quantity scalar
"""
if not progress:
progress = ProgressIndicator()
x = train.rescale(optimize_steps.units)
N = len(train)
C = {}
sampling_rate = 1024.0 / (x.t_stop - x.t_start)
dt = float(1.0 / sampling_rate)
y_hist = tools.bin_spike_trains({0: [x]}, sampling_rate)[0][0][0]
y_hist = sp.asfarray(y_hist) / N / dt
for step in optimize_steps:
s = float(step)
yh = sigproc.smooth(
y_hist, sigproc.GaussianKernel(2 * step), sampling_rate, num_bins=2048,
ensure_unit_area=True) * optimize_steps.units
# Equation from Matlab code, 7/2012
c = (sp.sum(yh ** 2) * dt -
2 * sp.sum(yh * y_hist) * dt +
2 * 1 / sp.sqrt(2 * sp.pi) / s / N)
C[s] = c * N * N
progress.step()
# Return kernel size with smallest cost
return min(C, key=C.get) * optimize_steps.units
```