def test_complexcoherence(self):
data = numpy.random.random((10, 10))
ts = time_series.TimeSeries(data=data)
dt = spectral.ComplexCoherenceSpectrum(source=ts,
array_data = numpy.random.random((10, 10)),
cross_spectrum = numpy.random.random((10, 10)),
epoch_length = 10,
segment_length = 5)
summary_info = dt.summary_info
self.assertEqual(summary_info['Frequency step'], 0.2)
self.assertEqual(summary_info['Maximum frequency'], 0.5)
self.assertEqual(summary_info['Source'], '')
self.assertEqual(summary_info['Spectral type'], 'ComplexCoherenceSpectrum')
self.assertTrue(dt.aggregation_functions is None)
self.assertEqual(dt.epoch_length, 10)
self.assertEqual(dt.segment_length, 5)
self.assertEqual(dt.shape, (10, 10))
self.assertTrue(dt.source is not None)
self.assertEqual(dt.windowing_function, '')
def test_complexcoherence(self):
data = numpy.random.random((10, 10))
ts = time_series.TimeSeries(data=data, title='meh')
dt = spectral.ComplexCoherenceSpectrum(source=ts,
windowing_function=str(''),
array_data=numpy.random.random((10, 10)),
cross_spectrum=numpy.random.random((10, 10)),
epoch_length=10,
segment_length=5)
summary_info = dt.summary_info()
assert summary_info['Frequency step'] == 0.2
assert summary_info['Maximum frequency'] == 0.5
assert summary_info['Source'] == 'meh'
assert summary_info['Spectral type'] == 'ComplexCoherenceSpectrum'
assert dt.epoch_length == 10
assert dt.segment_length == 5
assert dt.array_data.shape, (10 == 10)
assert dt.source is not None
assert dt.windowing_function is not None
def evaluate(self):
"""
Calculate the FFT, Cross Coherence and Complex Coherence of time_series
broken into (possibly) epochs and segments of length `epoch_length` and
`segment_length` respectively, filtered by `window_function`.
"""
cls_attr_name = self.__class__.__name__ + ".time_series"
# self.time_series.trait["data"].log_debug(owner=cls_attr_name)
tpts = self.time_series.data.shape[0]
time_series_length = tpts * self.time_series.sample_period
if len(self.time_series.data.shape) > 2:
time_series_data = numpy.squeeze(
(self.time_series.data.mean(axis=-1)).mean(axis=1))
# Divide time-series into epochs, no overlapping
if self.epoch_length > 0.0:
nepochs = int(numpy.floor(time_series_length / self.epoch_length))
epoch_tpts = int(self.epoch_length /
self.time_series.sample_period)
time_series_length = self.epoch_length
tpts = epoch_tpts
else:
self.epoch_length = time_series_length
nepochs = int(numpy.ceil(time_series_length / self.epoch_length))
# Segment time-series, overlapping if necessary
nseg = int(numpy.floor(time_series_length / self.segment_length))
if nseg > 1:
seg_tpts = int(self.segment_length /
self.time_series.sample_period)
seg_shift_tpts = int(self.segment_shift /
self.time_series.sample_period)
nseg = int(numpy.floor((tpts - seg_tpts) / seg_shift_tpts) + 1)
else:
self.segment_length = time_series_length
seg_tpts = time_series_data.shape[0]
# Frequency
nfreq = int(
numpy.min([
self.max_freq,
numpy.floor((seg_tpts + self.zeropad) / 2.0) + 1
]))
result_shape, av_result_shape = self.result_shape(
self.time_series.data.shape, self.max_freq, self.epoch_length,
self.segment_length, self.segment_shift,
self.time_series.sample_period, self.zeropad,
self.average_segments)
cs = numpy.zeros(result_shape, dtype=numpy.complex128)
av = numpy.matrix(numpy.zeros(av_result_shape, dtype=numpy.complex128))
coh = numpy.zeros(result_shape, dtype=numpy.complex128)
# Apply windowing function
if self.window_function is not None:
if self.window_function not in SUPPORTED_WINDOWING_FUNCTIONS:
self.log.error("Windowing function is: %s" %
self.window_function)
self.log.error("Must be in: %s" %
str(SUPPORTED_WINDOWING_FUNCTIONS))
window_function = eval("".join(("numpy.", self.window_function)))
win = window_function(seg_tpts)
window_mask = (numpy.kron(
numpy.ones((time_series_data.shape[1], 1)), win)).T
nave = 0
for j in numpy.arange(nepochs):
data = time_series_data[j * epoch_tpts:(j + 1) * epoch_tpts, :]
for i in numpy.arange(nseg): # average over all segments;
time_series = data[i * seg_shift_tpts:i * seg_shift_tpts +
seg_tpts, :]
if self.detrend_ts:
time_series = sp_signal.detrend(time_series, axis=0)
datalocfft = numpy.fft.fft(time_series * window_mask, axis=0)
datalocfft = numpy.matrix(datalocfft)
for f in numpy.arange(nfreq): # for all frequencies
if self.npat == 1:
if not self.average_segments:
cs[:, :, f, i] += numpy.conjugate(
datalocfft[f, :].conj().T * datalocfft[f, :])
av[:, f,
i] += numpy.conjugate(datalocfft[f, :].conj().T)
else:
cs[:, :, f] += numpy.conjugate(
datalocfft[f, :].conj().T * datalocfft[f, :])
av[:,
f] += numpy.conjugate(datalocfft[f, :].conj().T)
else:
if not self.average_segments:
cs[:, :, f, j, i] = numpy.conjugate(
datalocfft[f, :].conj().T * datalocfft[f, :])
av[:, f, j,
i] = numpy.conjugate(datalocfft[f, :].conj().T)
else:
cs[:, :, f, j] += numpy.conjugate(
datalocfft[f, :].conj().T * datalocfft[f, :])
av[:, f,
j] += numpy.conjugate(datalocfft[f, :].conj().T)
del datalocfft
nave += 1.0
# End of FORs
if not self.average_segments:
cs = cs / nave
av = av / nave
else:
nave = nave * nseg
cs = cs / nave
av = av / nave
# Subtract average
for f in numpy.arange(nfreq):
if self.subtract_epoch_average:
if self.npat == 1:
if not self.average_segments:
for i in numpy.arange(nseg):
cs[:, :, f,
i] = cs[:, :, f,
i] - av[:, f, i] * av[:, f, i].conj().T
else:
cs[:, :,
f] = cs[:, :, f] - av[:, f] * av[:, f].conj().T
else:
if not self.average_segments:
for i in numpy.arange(nseg):
for j in numpy.arange(nepochs):
cs[:, :, f, j,
i] = cs[:, :, f, j,
i] - av[:, f, j, i] * av[:, f, j,
i].conj().T
else:
for j in numpy.arange(nepochs):
cs[:, :, f,
j] = cs[:, :, f,
j] - av[:, f, j] * av[:, f, j].conj().T
# Compute Complex Coherence
ndim = len(cs.shape)
if ndim == 3:
for i in numpy.arange(cs.shape[2]):
temp = numpy.matrix(cs[:, :, i])
coh[:, :, i] = cs[:, :, i] / numpy.sqrt(
temp.diagonal().conj().T * temp.diagonal())
elif ndim == 4:
for i in numpy.arange(cs.shape[2]):
for j in numpy.arange(cs.shape[3]):
temp = numpy.matrix(numpy.squeeze(cs[:, :, i, j]))
coh[:, :, i, j] = temp / numpy.sqrt(
temp.diagonal().conj().T * temp.diagonal().T)
self.log.debug("result")
self.log.debug(narray_describe(cs))
spectra = spectral.ComplexCoherenceSpectrum(
source=self.time_series,
array_data=coh,
cross_spectrum=cs,
epoch_length=self.epoch_length,
segment_length=self.segment_length,
windowing_function=self.window_function)
return spectra
def calculate_complex_cross_coherence(time_series, epoch_length, segment_length, segment_shift, window_function,
average_segments, subtract_epoch_average, zeropad, detrend_ts, max_freq,
npat):
"""
# type: (TimeSeries, float, float, float, str, bool, bool, int, bool, float, float) -> ComplexCoherenceSpectrum
Calculate the FFT, Cross Coherence and Complex Coherence of time_series
broken into (possibly) epochs and segments of length `epoch_length` and
`segment_length` respectively, filtered by `window_function`.
Parameters
__________
time_series : TimeSeries
The timeseries for which the CrossCoherence and ComplexCoherence is to be computed.
epoch_length : float
In general for lengthy EEG recordings (~30 min), the timeseries are divided into equally
sized segments (~ 20-40s). These contain the event that is to be characterized by means of the
cross coherence. Additionally each epoch block will be further divided into segments to which
the FFT will be applied.
segment_length : float
The segment length determines the frequency resolution of the resulting power spectra --
longer windows produce finer frequency resolution.
segment_shift : float
Time length by which neighboring segments are shifted. e.g.
`segment shift` = `segment_length` / 2 means 50% overlapping segments.
window_function : str
Windowing functions can be applied before the FFT is performed.
average_segments : bool
Flag. If `True`, compute the mean Cross Spectrum across segments.
subtract_epoch_average: bool
Flag. If `True` and if the number of epochs is > 1, you can optionally subtract the
mean across epochs before computing the complex coherence.
zeropad : int
Adds `n` zeros at the end of each segment and at the end of window_function. It is not yet functional.
detrend_ts : bool
Flag. If `True` removes linear trend along the time dimension before applying FFT.
max_freq : float
Maximum frequency points (e.g. 32., 64., 128.) represented in the output. Default is segment_length / 2 + 1.
npat : float
This attribute appears to be related to an input projection matrix... Which is not yet implemented.
"""
# self.time_series.trait["data"].log_debug(owner=cls_attr_name)
tpts = time_series.data.shape[0]
time_series_length = tpts * time_series.sample_period
if len(time_series.data.shape) > 2:
time_series_data = numpy.squeeze((time_series.data.mean(axis=-1)).mean(axis=1))
# Divide time-series into epochs, no overlapping
if epoch_length > 0.0:
nepochs = int(numpy.floor(time_series_length / epoch_length))
epoch_tpts = int(epoch_length / time_series.sample_period)
time_series_length = epoch_length
tpts = epoch_tpts
else:
epoch_length = time_series_length
nepochs = int(numpy.ceil(time_series_length / epoch_length))
# Segment time-series, overlapping if necessary
nseg = int(numpy.floor(time_series_length / segment_length))
if nseg > 1:
seg_tpts = int(segment_length / time_series.sample_period)
seg_shift_tpts = int(segment_shift / time_series.sample_period)
nseg = int(numpy.floor((tpts - seg_tpts) / seg_shift_tpts) + 1)
else:
segment_length = time_series_length
seg_tpts = time_series_data.shape[0]
# Frequency
nfreq = int(numpy.min([max_freq, numpy.floor((seg_tpts + zeropad) / 2.0) + 1]))
resulted_shape, av_result_shape = complex_coherence_result_shape(time_series.data.shape, max_freq, epoch_length,
segment_length, segment_shift,
time_series.sample_period, zeropad,
average_segments)
cs = numpy.zeros(resulted_shape, dtype=numpy.complex128)
av = numpy.matrix(numpy.zeros(av_result_shape, dtype=numpy.complex128))
coh = numpy.zeros(resulted_shape, dtype=numpy.complex128)
# Apply windowing function
if window_function is not None:
if window_function not in SUPPORTED_WINDOWING_FUNCTIONS:
log.error("Windowing function is: %s" % window_function)
log.error("Must be in: %s" % str(SUPPORTED_WINDOWING_FUNCTIONS))
window_func = eval("".join(("numpy.", window_function)))
win = window_func(seg_tpts)
window_mask = (numpy.kron(numpy.ones((time_series_data.shape[1], 1)), win)).T
nave = 0
for j in numpy.arange(nepochs):
data = time_series_data[j * epoch_tpts:(j + 1) * epoch_tpts, :]
for i in numpy.arange(nseg): # average over all segments;
ts = data[i * seg_shift_tpts: i * seg_shift_tpts + seg_tpts, :]
if detrend_ts:
ts = sp_signal.detrend(ts, axis=0)
datalocfft = numpy.fft.fft(ts * window_mask, axis=0)
datalocfft = numpy.matrix(datalocfft)
for f in numpy.arange(nfreq): # for all frequencies
if npat == 1:
if not average_segments:
cs[:, :, f, i] += numpy.conjugate(datalocfft[f, :].conj().T * datalocfft[f, :])
av[:, f, i] += numpy.conjugate(datalocfft[f, :].conj().T)
else:
cs[:, :, f] += numpy.conjugate(datalocfft[f, :].conj().T * datalocfft[f, :])
av[:, f] += numpy.conjugate(datalocfft[f, :].conj().T)
else:
if not average_segments:
cs[:, :, f, j, i] = numpy.conjugate(datalocfft[f, :].conj().T * datalocfft[f, :])
av[:, f, j, i] = numpy.conjugate(datalocfft[f, :].conj().T)
else:
cs[:, :, f, j] += numpy.conjugate(datalocfft[f, :].conj().T * datalocfft[f, :])
av[:, f, j] += numpy.conjugate(datalocfft[f, :].conj().T)
del datalocfft
nave += 1.0
# End of FORs
if not average_segments:
cs = cs / nave
av = av / nave
else:
nave = nave * nseg
cs = cs / nave
av = av / nave
# Subtract average
for f in numpy.arange(nfreq):
if subtract_epoch_average:
if npat == 1:
if not average_segments:
for i in numpy.arange(nseg):
cs[:, :, f, i] = cs[:, :, f, i] - av[:, f, i] * av[:, f, i].conj().T
else:
cs[:, :, f] = cs[:, :, f] - av[:, f] * av[:, f].conj().T
else:
if not average_segments:
for i in numpy.arange(nseg):
for j in numpy.arange(nepochs):
cs[:, :, f, j, i] = cs[:, :, f, j, i] - av[:, f, j, i] * av[:, f, j, i].conj().T
else:
for j in numpy.arange(nepochs):
cs[:, :, f, j] = cs[:, :, f, j] - av[:, f, j] * av[:, f, j].conj().T
# Compute Complex Coherence
ndim = len(cs.shape)
if ndim == 3:
for i in numpy.arange(cs.shape[2]):
temp = numpy.matrix(cs[:, :, i])
coh[:, :, i] = cs[:, :, i] / numpy.sqrt(temp.diagonal().conj().T * temp.diagonal())
elif ndim == 4:
for i in numpy.arange(cs.shape[2]):
for j in numpy.arange(cs.shape[3]):
temp = numpy.matrix(numpy.squeeze(cs[:, :, i, j]))
coh[:, :, i, j] = temp / numpy.sqrt(temp.diagonal().conj().T * temp.diagonal().T)
log.debug("result")
log.debug(narray_describe(cs))
spectra = spectral.ComplexCoherenceSpectrum(source=time_series,
array_data=coh,
cross_spectrum=cs,
epoch_length=epoch_length,
segment_length=segment_length,
windowing_function=window_function)
return spectra