def spike_density_estimation(trains, start=0*pq.ms, stop=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 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 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
else:
units = optimize_steps.units
# Prepare evaluation points
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
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)
ksize = float(kernel_size[u])
# Create density estimation using convolution
kde[u] = _train_density(collapsed.time_slice(start, stop),
kernel, ksize) / len(trains[u]) / units
kde[u].units = pq.Hz
return kde, kernel_size, eval_points
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
def correlogram(trains, bin_size, max_lag=500 * pq.ms, border_correction=True,
per_second=True, unit=pq.ms, progress=None):
""" Return (cross-)correlograms from a dictionary of spike train
lists for different units.
:param dict trains: Dictionary of :class:`neo.core.SpikeTrain` lists.
:param bin_size: Bin size (time).
:type bin_size: Quantity scalar
:param max_lag: Cut off (end time of calculated correlogram).
:type max_lag: Quantity scalar
:param bool border_correction: Apply correction for less data at higher
timelags. Not perfect for bin_size != 1*``unit``, especially with
large ``max_lag`` compared to length of spike trains.
:param bool per_second: If ``True``, counts returned are per second.
Otherwise, counts per spike train are returned.
:param Quantity unit: Unit of X-Axis.
:param progress: A ProgressIndicator object for the operation.
:type progress: :class:`.progress_indicator.ProgressIndicator`
:returns: Two values:
* An ordered dictionary indexed with the indices of ``trains`` of
ordered dictionaries indexed with the same indices. Entries of
the inner dictionaries are the resulting (cross-)correlograms as
numpy arrays. All crosscorrelograms can be indexed in two
different ways: ``c[index1][index2]`` and ``c[index2][index1]``.
* The bins used for the correlogram calculation.
:rtype: dict, Quantity 1D
"""
if not progress:
progress = ProgressIndicator()
bin_size.rescale(unit)
max_lag.rescale(unit)
# Create bins, making sure that 0 is at the center of central bin
half_bins = sp.arange(bin_size / 2, max_lag, bin_size)
all_bins = list(reversed(-half_bins))
all_bins.extend(half_bins)
bins = sp.array(all_bins) * unit
middle_bin = len(bins) / 2 - 1
indices = trains.keys()
num_trains = len(trains[indices[0]])
if not num_trains:
raise SpykeException('Could not create correlogram: No spike trains!')
for u in range(1, len(indices)):
if len(trains[indices[u]]) != num_trains:
raise SpykeException('Could not create correlogram: All units ' +
'need the same number of spike trains!')
progress.set_ticks(sp.sum(range(len(trains) + 1) * num_trains))
corrector = 1
if border_correction:
# Need safe min/max functions
def safe_max(seq):
if len(seq) < 1:
return 0
return max(seq)
def safe_min(seq):
if len(seq) < 1:
return 2 ** 22 # Some arbitrary large value
return min(seq)
max_w = max([max([safe_max(t) for t in l])
for l in trains.itervalues()])
min_w = min([min([safe_min(t) for t in l])
for l in trains.itervalues()])
train_length = (max_w - min_w)
l = int(round(middle_bin)) + 1
cE = max(train_length - (l * bin_size) + 1 * unit, 1 * unit)
corrector = (train_length / sp.concatenate(
(sp.linspace(cE, train_length, l - 1, False),
sp.linspace(train_length, cE, l)))).magnitude
correlograms = OrderedDict()
for i1 in xrange(len(indices)): # For each index
# For all later indices, including itself
for i2 in xrange(i1, len(indices)):
histogram = sp.zeros(len(bins) - 1)
for t in xrange(num_trains):
train1 = trains[indices[i1]][t].rescale(unit).reshape((1, -1))
train2 = trains[indices[i2]][t].rescale(unit).reshape((-1, 1))
histogram += sp.histogram(
sp.subtract(train1, train2), bins=bins)[0]
if i1 == i2: # Correction for autocorrelogram
histogram[middle_bin] -= len(train2)
progress.step()
if per_second:
l = train1.t_stop - train1.t_start
if train2.t_stop - train2.t_start != l:
raise SpykeException(
'A spike train pair does not have equal length,'
'cannot calculate count per second.')
histogram /= l.rescale(pq.s)
crg = corrector * histogram / num_trains
if indices[i1] not in correlograms:
correlograms[indices[i1]] = OrderedDict()
correlograms[indices[i1]][indices[i2]] = crg
if i1 != i2:
if indices[i2] not in correlograms:
correlograms[indices[i2]] = OrderedDict()
correlograms[indices[i2]][indices[i1]] = crg[::-1]
return correlograms, bins
def spike_amplitude_histogram(trains, num_bins, uniform_y_scale=True, unit=pq.uV, progress=None):
""" Return a spike amplitude histogram.
The resulting is useful to assess the drift in spike amplitude over a
longer recording. It shows histograms (one for each ``trains`` entry,
e.g. segment) of maximum and minimum spike amplitudes.
:param list trains: A list of lists of :class:`neo.core.SpikeTrain`
objects. Each entry of the outer list will be one point on the
x-axis (they could correspond to segments), all amplitude occurences
of spikes contained in the inner list will be added up.
:param int num_bins: Number of bins for the histograms.
:param bool uniform_y_scale: If True, the histogram for each channel
will use the same bins. Otherwise, the minimum bin range is computed
separately for each channel.
:param Quantity unit: Unit of Y-Axis.
:param progress: Set this parameter to report progress.
:type progress: :class:`spykeutils.progress_indicator.ProgressIndicator`
:return: A tuple with three values:
* A three-dimensional histogram matrix, where the first dimension
corresponds to bins, the second dimension to the entries of
``trains`` (e.g. segments) and the third dimension to channels.
* A list of the minimum amplitude value for each channel (all values
will be equal if ``uniform_y_scale`` is true).
* A list of the maximum amplitude value for each channel (all values
will be equal if ``uniform_y_scale`` is true).
:rtype: (ndarray, list, list)
"""
if not progress:
progress = ProgressIndicator()
num_channels = 1
for t in trains:
if not t:
continue
num_channels = t[0].waveforms.shape[2]
break
progress.set_ticks(2 * len(trains))
progress.set_status("Calculating Spike Amplitude Histogram")
# Find maximum and minimum amplitudes on all channels
up = [0] * num_channels
down = [0] * num_channels
for t in trains:
for s in t:
if s.waveforms is None:
continue
if s.waveforms.shape[2] != num_channels:
raise SpykeException(
"All spikes need to have the same " + "numer of channels for Spike Amplitude Histogram!"
)
a = sp.asarray(s.waveforms.rescale(unit))
u = a.max(1)
d = a.min(1)
for c in xrange(num_channels):
up[c] = max(up[c], sp.stats.mstats.mquantiles(u[:, c], [0.999])[0])
down[c] = min(down[c], sp.stats.mstats.mquantiles(d[:, c], [0.001])[0])
progress.step()
if uniform_y_scale:
up = [max(up)] * num_channels
down = [min(down)] * num_channels
# Create histogram
bins = [sp.linspace(down[c], up[c], num_bins + 1) for c in xrange(num_channels)]
hist = sp.zeros((num_bins, len(trains), num_channels))
for i, t in enumerate(trains):
for s in t:
if s.waveforms is None:
continue
a = sp.asarray(s.waveforms.rescale(unit))
upper = a.max(1)
lower = a.min(1)
for c in xrange(num_channels):
hist[:, i, c] += sp.histogram(upper[:, c], bins[c])[0]
hist[:, i, c] += sp.histogram(lower[:, c], bins[c])[0]
progress.step()
return hist, down, up
def spike_amplitude_histogram(trains, num_bins, uniform_y_scale=True,
unit=pq.uV, progress=None):
""" Return a spike amplitude histogram.
The resulting is useful to assess the drift in spike amplitude over a
longer recording. It shows histograms (one for each ``trains`` entry,
e.g. segment) of maximum and minimum spike amplitudes.
:param list trains: A list of lists of :class:`neo.core.SpikeTrain`
objects. Each entry of the outer list will be one point on the
x-axis (they could correspond to segments), all amplitude occurences
of spikes contained in the inner list will be added up.
:param int num_bins: Number of bins for the histograms.
:param bool uniform_y_scale: If True, the histogram for each channel
will use the same bins. Otherwise, the minimum bin range is computed
separately for each channel.
:param Quantity unit: Unit of Y-Axis.
:param progress: Set this parameter to report progress.
:type progress: :class:`.progress_indicator.ProgressIndicator`
:return: A tuple with three values:
* A three-dimensional histogram matrix, where the first dimension
corresponds to bins, the second dimension to the entries of
``trains`` (e.g. segments) and the third dimension to channels.
* A list of the minimum amplitude value for each channel (all values
will be equal if ``uniform_y_scale`` is true).
* A list of the maximum amplitude value for each channel (all values
will be equal if ``uniform_y_scale`` is true).
:rtype: (ndarray, list, list)
"""
if not progress:
progress = ProgressIndicator()
num_channels = 1
for t in trains:
if not t:
continue
num_channels = t[0].waveforms.shape[2]
break
progress.set_ticks(2*len(trains))
progress.set_status('Calculating Spike Amplitude Histogram')
# Find maximum and minimum amplitudes on all channels
up = [0] * num_channels
down = [0] * num_channels
for t in trains:
for s in t:
if s.waveforms is None:
continue
if s.waveforms.shape[2] != num_channels:
raise SpykeException('All spikes need to have the same ' +
'numer of channels for Spike Amplitude Histogram!')
a = sp.asarray(s.waveforms.rescale(unit))
u = a.max(1)
d = a.min(1)
for c in xrange(num_channels):
up[c] = max(up[c], sp.stats.mstats.mquantiles(
u[:,c], [0.999])[0])
down[c] = min(down[c], sp.stats.mstats.mquantiles(
d[:,c], [0.001])[0])
progress.step()
if uniform_y_scale:
up = [max(up)] * num_channels
down = [min(down)] * num_channels
# Create histogram
bins = [sp.linspace(down[c],up[c], num_bins+1)
for c in xrange(num_channels)]
hist = sp.zeros((num_bins, len(trains), num_channels))
for i, t in enumerate(trains):
for s in t:
if s.waveforms is None:
continue
a = sp.asarray(s.waveforms.rescale(unit))
upper = a.max(1)
lower = a.min(1)
for c in xrange(num_channels):
hist[:,i,c] += sp.histogram(upper[:,c], bins[c])[0]
hist[:,i,c] += sp.histogram(lower[:,c], bins[c])[0]
progress.step()
return hist, down, up