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
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
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:`spykeutils.progress_indicator.ProgressIndicator`
:returns: Best of the given kernel sizes
:rtype: Quantity scalar
"""
if not progress:
progress = ProgressIndicator()
x = train.rescale(optimize_steps.units)
steps = sp.asarray(optimize_steps)
N = len(train)
C = {}
bins = sp.linspace(x.t_start, x.t_stop, 1025)
dt = float(bins[1] - bins[0])
y_hist = sp.histogram(x, bins)[0] / N / dt
for step in steps:
s = float(step)
yh = _hist_density(y_hist, gauss_kernel, step,
train.t_start, train.t_stop)
# 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)*train.units
def get_refperiod_violations(spike_trains, refperiod, progress=None):
""" Return the refractory period violations in the given spike trains
for the specified refractory period.
:param dict spike_trains: Dictionary of lists of
:class:`neo.core.SpikeTrain` objects.
:param refperiod: The refractory period (time).
:type refperiod: Quantity scalar
:param progress: Set this parameter to report progress.
:type progress: :class:`.progress_indicator.ProgressIndicator`
:returns: Two values:
* The total number of violations.
* A dictionary (with the same indices as ``spike_trains``) of
arrays with violation times (Quantity 1D with the same unit as
``refperiod``) for each spike train.
:rtype: int, dict """
if type(refperiod) != pq.Quantity or \
refperiod.simplified.dimensionality != pq.s.dimensionality:
raise ValueError('refperiod must be a time quantity!')
if not progress:
progress = ProgressIndicator()
total_violations = 0
violations = {}
for u, tL in spike_trains.iteritems():
violations[u] = []
for i, t in enumerate(tL):
st = t.copy()
st.sort()
isi = sp.diff(st)
violations[u].append(st[isi < refperiod].rescale(refperiod.units))
total_violations += len(violations[u][i])
progress.step()
return total_violations, violations
def get_refperiod_violations(spike_trains, refperiod, progress=None):
""" Return the refractory period violations in the given spike trains
for the specified refractory period.
:param dict spike_trains: Dictionary of lists of
:class:`neo.core.SpikeTrain` objects.
:param refperiod: The refractory period (time).
:type refperiod: Quantity scalar
:param progress: Set this parameter to report progress.
:type progress: :class:`.progress_indicator.ProgressIndicator`
:returns: Two values:
* The total number of violations.
* A dictionary (with the same indices as ``spike_trains``) of
arrays with violation times (Quantity 1D with the same unit as
``refperiod``) for each spike train.
:rtype: int, dict """
if type(refperiod) != pq.Quantity or refperiod.simplified.dimensionality != pq.s.dimensionality:
raise ValueError("refperiod must be a time quantity!")
if not progress:
progress = ProgressIndicator()
total_violations = 0
violations = {}
for u, tL in spike_trains.iteritems():
violations[u] = []
for i, t in enumerate(tL):
st = t.copy()
st.sort()
isi = sp.diff(st)
violations[u].append(st[isi < refperiod].rescale(refperiod.units))
total_violations += len(violations[u][i])
progress.step()
return total_violations, violations
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 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:`.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