def coherence(self, other, width, overlap=0, **kwargs):
"""
Compute the short-time correlation coefficient of the signal. Uses the function
:func:`scipy.signal.coherence` for this computation.
Parameters
----------
other : Signal
The other Signal that will be used to perform the short time cross correlation.
width : float
Window size (in Signal index units) that will be used in computing the short-time
correlation coefficient.
overlap : float, optional
Units (index units) of overlap between consecutive computations.
Returns
-------
: array_like
The computed short tiem cross-correlation function.
"""
other = other(self.index)
nperseg = int(width * self.fs)
nol = int(overlap * self.fs)
f, cxy = coherence(self.values, other.values, self.fs, nperseg=nperseg, noverlap=nol,
**kwargs)
return Signal(cxy, index=f)
def coherence_plot(df):
r"""Returns a plot showing the coherence matrix.
Parameters
----------
df : a pandas data frame
Must indicies and column data set to the timestampls and eeg channel names.
Returns
-------
html
HTML code for the plot.
"""
df = df.ix[::100]
currd = df.as_matrix()
currd = currd.T
coherearr = []
for i in range (0, len(currd)):
temparr = []
for j in range (0, len(currd)):
temparr.append(np.mean(
signal.coherence(currd[i], currd[j], 500)[1]
))
coherearr.append(temparr)
df = pd.DataFrame(data=np.array(coherearr), index=df.columns, columns=df.columns)
fig = df.iplot(kind='heatmap',
theme='solar', asFigure=True)
fig.layout.update(dict(title="Coherence", height=800, width=800))
colorscale = [[0, '#0000FF'],[.5, '#FFFFFF'], [1, '#FF0000']] # custom colorscale
fig.data.update(
dict(colorscale=colorscale, showscale = True,
colorbar=dict(title="coherence")))
return fig
def computeCoherenceFeatures(lfp_data, channel_pairs, Fs, power_bands, event_indices, t_window): ''' Inputs - lfp_data: dictionary of data, with one entry for each channel - channel_pairs: list of channel pairs - Fs: sampling frequency - power_bands: list of power bands - event_indices: N x M array of event indices, where N is the number of trials and M is the number of different events - t_window: length M array of time window (in seconds) to compute features over, one element for each feature Outputs - features: dictionary with N entries (one per trial), with a C x K matric which C is the number of channel pairs and K is the number of features (number of power bands times M) ''' nperseg = int(Fs*0.25) noverlap = int(Fs*0.1875) t_window = [int(Fs*time) for time in t_window] # changing seconds into samples N, M = event_indices.shape times = np.ones([N,M]) for t,time in enumerate(t_window): times[:,t] = time*np.ones(N) features = dict() channels = lfp_data.keys() num_channel_pairs = len(channel_pairs) for trial in range(0,N): events = event_indices[trial,:] # should be array of length M trial_powers = np.zeros([num_channel_pairs,M*len(power_bands)]) for j, pair in enumerate(channel_pairs): chann1 = pair[0] chann2 = pair[1] chann_data1 = lfp_data[chann1] chann_data2 = lfp_data[chann2] feat_counter = 0 for i,ind in enumerate(events): data1 = chann_data1[ind:ind + times[trial,i]] data1 = np.ravel(data1) data2 = chann_data2[ind:ind + times[trial,i]] data2 = np.ravel(data2) f, Cxy = signal.coherence(data1, data2, nperseg = nperseg, fs=Fs, noverlap=noverlap) #Cxy = Cxy/np.sum(Cxy) #Cxy = 10*np.log10(Cxy) Cxy = np.sqrt(Cxy) for k in range(0,len(power_bands)): low_band, high_band = power_bands[k] freqs = np.ravel(np.nonzero(np.greater(f,low_band)&np.less_equal(f,high_band))) tot_power_band = np.sum(Cxy[freqs]) trial_powers[j,feat_counter] = tot_power_band #trial_powers[j,i*len(power_bands) + k] = np.sum(tot_power_band)/float(len(tot_power_band)) feat_counter += 1 features[str(trial)] = trial_powers return features
def test_identical_input(self):
x = np.random.randn(20)
y = np.copy(x) # So `y is x` -> False
f = np.linspace(0, 0.5, 6)
C = np.ones(6)
f1, C1 = coherence(x, y, nperseg=10)
assert_allclose(f, f1)
assert_allclose(C, C1)
def test_phase_shifted_input(self):
x = np.random.randn(20)
y = -x
f = np.linspace(0, 0.5, 6)
C = np.ones(6)
f1, C1 = coherence(x, y, nperseg=10)
assert_allclose(f, f1)
assert_allclose(C, C1)
def get_coherence(s1,s2,sampling=5000):
""" Gets the coherence between signals s1 and s2
Input:
s1,s2: two time series
sampling: the sampling of the signal [def: 5000]
Output:
Cxy
"""
from scipy.signal import coherence
return coherence(s1,s2,sampling=sampling)
def CalcCoherence(x,y):
fs = 500
f, Cxy = signal.coherence(x, y, fs, nperseg=256, noverlap = 128, detrend = False)
plt.semilogy(f, Cxy, alpha = 0.2)
plt.xlabel('frequency [Hz]')
plt.ylabel('Coherence')
plt.show()
# equivalent degrees of freedom: (length(timeseries)/windowhalfwidth)*mean_coherence
# calculate 95% confidence level
edof = (len(x)/(256/2)) * Cxy.mean()
gamma95 = 1.-(0.05)**(1./(edof-1.))
print(gamma95)
return np.array(Cxy)
def _pipe_as_flow(self, signal_packet):
# Get signal_packet details
hkey = signal_packet.keys()[0]
ax_0_ix = signal_packet[hkey]['meta']['ax_0']['index']
ax_1_ix = signal_packet[hkey]['meta']['ax_1']['index']
signal = signal_packet[hkey]['data']
fs = np.int(np.mean(1./np.diff(ax_0_ix)))
# Assume undirected connectivity
triu_ix, triu_iy = np.triu_indices(len(ax_1_ix), k=1)
# Initialize association matrix
adj = np.zeros((len(ax_1_ix), len(ax_1_ix)))
# Derive signal segmenting for coherence estimation
nperseg = int(self.secperseg*fs)
noverlap = int(self.secperseg*fs*self.pctoverlap)
freq, Cxy = coherence(signal[:, triu_ix],
signal[:, triu_iy],
fs=fs, window=self.window,
nperseg=nperseg, noverlap=noverlap,
axis=0)
# Find closest frequency to the desired center frequency
cf_idx = np.flatnonzero((freq >= self.cf[0]) &
(freq <= self.cf[1]))
# Store coherence in association matrix
adj[triu_ix, triu_iy] = np.mean(Cxy[cf_idx, :], axis=0)
adj += adj.T
new_packet = {}
new_packet[hkey] = {
'data': adj,
'meta': {
'ax_0': signal_packet[hkey]['meta']['ax_1'],
'ax_1': signal_packet[hkey]['meta']['ax_1'],
'time': {
'label': 'Time (sec)',
'index': np.float(ax_0_ix[-1])
}
}
}
return new_packet
def get_coherence(filename1, filename2):
f1_data, f1_sample_rate = get_file_data(filename1)
f2_data, f2_sample_rate = get_file_data(filename2)
if f1_sample_rate != f2_sample_rate:
print("Sample rates of the signals differ but have to be the same. Exiting... ")
return
else:
sample_rate = f1_sample_rate
f, coherence = signal.coherence(f1_data, f2_data, sample_rate, nperseg = 128)
plot.gca().set_ylim([0.000001, 100])
plot.semilogy(f, coherence)
len_coherence = len(coherence)
print("coherence vector len: {0}".format(len_coherence))
print(coherence)
sum_coherence = sum(coherence)
print("coherence vector sum: {0}".format(sum_coherence))
similarity = int(sum_coherence/len_coherence * 100.0)
print("similarity(%): {0}".format(similarity))
distorsion = 1 - coherence
distorsion_avg = np.mean(distorsion)
distorsion_std = np.std(distorsion)
print("distorsion(%): {0:.1f} std: {1:.1f}".format(distorsion_avg * 100, distorsion_std * 100))
log_coherence = abs(np.log10(coherence))
log_coherence_sum = sum(log_coherence)
print(log_coherence)
# the numbers have been gotten from my personal observations
threshold_mean = 1 # mean not more than 0.9 (1 - 0.9 = 1)
threshold_std = 0.5 # with std dev not more than 0.5
coh_sum = log_coherence_sum
coh_mean = np.mean(log_coherence)
coh_std = np.std(log_coherence)
print(
"log coherence sum: {0:.1f} "
"mean: {1:.1f} std: {2:.1f}".
format(coh_sum, coh_mean, coh_std))
signal_is = "GOOD"
if coh_mean > threshold_mean or coh_std > threshold_std:
signal_is = "BAD"
print("The signal is {0}".format(signal_is))
plot.show()
def plot_coherence():
casts = np.r_[92:123]
# 33 comes from nperseg of 64
coheres = np.zeros((len(casts), 33))
for i, cast_num in enumerate(casts):
C, sigma, theta, p, S, T = read_cast(cast_num)
f, cohere = coherence(C, T, fs=24, nperseg=64)
coheres[i] = cohere
cohere_bins = np.r_[0:1:11j]
cohere_f = np.zeros((f.size, cohere_bins.size - 1))
for i, cohere_i in enumerate(coheres.T):
cohere_f[i] = np.histogram(cohere_i, cohere_bins, density=True)[0]
# Exact details need work. Mostly wanted to see at what frequency
# coherence clearly starts to decrease
# I'd say 4Hz
plt.pcolormesh(f, cohere_bins, cohere_f.T, cmap='afmhot_r', vmax=4)
return coheres
def Coherence(ts1, ts2, fs, dt):
"""Compute magnitude squared coherence (using coherence)"""
# Gapfill the missing value
mk1 = np.isnan(ts1)
mk2 = np.isnan(ts2)
ts1[mk1 == True] = nanmean(ts1)
ts1[mk2 == True] = nanmean(ts1)
ts2[mk1 == True] = nanmean(ts2)
ts2[mk2 == True] = nanmean(ts2)
nwindow = 9 # Number of windows to smooth data
length = math.floor(len(ts1) / nwindow) # Length calculated by deviding the window
nwindow_fl = math.floor(log2(length)) # Number of windows with floor window length
window = int(2 ** nwindow_fl) # segment_length
f, Cxy = signal.coherence(ts1, ts2, fs, nperseg=window, detrend=dt)
return [f, Cxy]
def coh(self, mode):
t, B, E = self.get('t'), self.get('B' + mode), self.get('E' + mode)
return signal.coherence(B, E, fs=1/( t[1] - t[0] ), nperseg=t.size/2,
noverlap=t.size/2 - 1)[1]
anue_nue_cohspec[r] = np.zeros((howmanyfreqs[r], howmanytimes[r]))
nue_nux_cohspec[r] = np.zeros((howmanyfreqs[r], howmanytimes[r]))
beginhere[r] = Nperseg[r] / 2 + 1
if mod(Nperseg[r], 2) == 0:
times_cspec[r] = t[r][beginhere[r]:-beginhere[r] + 1]
else:
times_cspec[r] = t[r][beginhere[r]:-beginhere[r]]
print 'Computing coherence spectrograms now'
for r in rotrates:
bh = beginhere[r]
getfreqs = 'yes'
for time in range(howmanytimes[r]):
bup = ss.coherence(gwc[r][time:time + Nperseg[r]],
anuec[r][time:time + Nperseg[r]],
fs=1. / dt[r],
window=(Window),
nperseg=Nperseg[r] / 2,
noverlap=Nperseg[r] / 2 - 1,
nfft=Nfft[r])
gw_anue_cohspec[r][:, time] = bup[1]
bup = ss.coherence(gwc[r][time:time + Nperseg[r]],
nuxc[r][time:time + Nperseg[r]],
fs=1. / dt[r],
window=(Window),
nperseg=Nperseg[r] / 2,
noverlap=Nperseg[r] / 2 - 1,
nfft=Nfft[r])
gw_nux_cohspec[r][:, time] = bup[1]
bup = ss.coherence(gwc[r][time:time + Nperseg[r]],
nuec[r][time:time + Nperseg[r]],
fs=1. / dt[r],
def parallel_coh(self, first_elect, sec_elect):
f_loop, Cxy_loop = coherence(self.volt_state[:, first_elect + 2],
self.volt_state[:, sec_elect + 2],
self.downsampling_rate,
nperseg=self.downfreq_ratio)
return f_loop, Cxy_loop
fs,
nperseg=windowSize,
noverlap=0,
scaling="spectrum")
fxy, xyPower = signal.csd(x,
y,
fs,
nperseg=windowSize,
noverlap=0,
scaling="spectrum")
welchCoh1 = np.power(np.absolute(xyPower), 2)
welchCoh2 = xPower * yPower
welchCoh = welchCoh1 / welchCoh2
f, Cxy = signal.coherence(x, y, fs, nperseg=windowSize, noverlap=N / 200)
f2, Cxy2 = signal.coherence(x, y, fs, nperseg=windowSize, noverlap=0)
# my method
powXX = np.zeros(shape=(fftSize), dtype="complex")
powYY = np.zeros(shape=(fftSize), dtype="complex")
powXY = np.zeros(shape=(fftSize), dtype="complex")
# win
winFnc = signal.hanning(windowSize)
winFnc = winFnc / winFnc.sum()
# save stacked
stackX = np.zeros(shape=(fftSize), dtype="complex")
stackY = np.zeros(shape=(fftSize), dtype="complex")
arrX = np.zeros(shape=(windows, fftSize), dtype="complex")
arrY = np.zeros(shape=(windows, fftSize), dtype="complex")
# We now have all the data that is either LH or LDO
if debug:
print(inv)
print(st)
## Sliding Window ##
for stT in st.slide(window_length=window, step=stepsize):
stT.detrend('constant')
## Here we grab the pressure and compute the coherence with the two different components ##
press = stT.select(channel='LDO')[0].data
if sta == 'WCI':
press = press*1.43*10**-2 + 8*10**4
else:
press = press*0.1
f,cxy1 = coherence(stT.select(channel='LH1')[0].data, press, nperseg=lenfft)
f,cxy2 = coherence(stT.select(channel='LH2')[0].data, press, nperseg=lenfft)
cmean = np.mean(np.array([cxy1[1:],cxy2[1:]]),axis=0)
f = f[1:]
cmean = cmean[(f>= fmin) & (f <= fmax)]
cmean = np.mean(cmean)
if 'c' not in vars():
c = cmean
else:
c = np.vstack((c, cmean))
c = np.vstack((c, cmean))
if net != 'XX':
stT.rotate(method="->ZNE", inventory=inv)
stT.filter('bandpass',freqmin=fmin, freqmax=fmax)
stT.taper(0.05)
if debug:
legend(loc=(1.02, 0.2))
ylabel('Variance (prop to)')
gca().set_xticklabels('')
subplot(313)
for ii, nn in enumerate(nomprsvec):
semilogx(frqall[frqind],
frqall[frqind] * psd['u'][nn][frqind],
label=str(nn) + ' db',
color=cm.YlGnBu(ii * 30 + 80))
xlabel('CPD')
savefig('../figures/VertModes/from_raw_data/VarSpec_' + moorname + '.png',
bbox_inches='tight')
fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, sharey=True, figsize=(10, 7))
for ii, nn in enumerate(nomprsvec):
f, Cxy = signal.coherence(pb, adat['v'].sel(nomprs=nn), nperseg=4096)
fday = f * 48
fint = fday < 0.8
ax1.semilogx(fday[fint],
Cxy[fint],
label=str(nn) + ' db',
color=cm.YlGnBu(ii * 30 + 80))
ax1.legend(loc=(1.02, 0.2))
ax1.set_ylabel('with meridional velocity')
for ii, nn in enumerate(nomprsvec):
f, Cxy = signal.coherence(pb, adat['v'].sel(nomprs=nn), nperseg=4096)
fday = f * 48
fint = fday < 0.8
ax2.plot(fday[fint],
Cxy[fint],
label=str(nn) + ' db',
ax = axes[0][1]
ax.plot(times, 1e9 * signal2, lw=0.5)
ax.set(xlabel='Time (s)', xlim=times[[0, -1]], title='Signal 2')
# Power spectrum of the first timeseries
f, p = welch(signal1, fs=sfreq, nperseg=128, nfft=256)
ax = axes[1][0]
# Only plot the first 100 frequencies
ax.plot(f[:100], 20 * np.log10(p[:100]), lw=1.)
ax.set(xlabel='Frequency (Hz)',
xlim=f[[0, 99]],
ylabel='Power (dB)',
title='Power spectrum of signal 1')
# Compute the coherence between the two timeseries
f, coh = coherence(signal1, signal2, fs=sfreq, nperseg=100, noverlap=64)
ax = axes[1][1]
ax.plot(f[:50], coh[:50], lw=1.)
ax.set(xlabel='Frequency (Hz)',
xlim=f[[0, 49]],
ylabel='Coherence',
title='Coherence between the timeseries')
fig.tight_layout()
###############################################################################
# Now we put the signals at two locations on the cortex. We construct a
# :class:`mne.SourceEstimate` object to store them in.
#
# The timeseries will have a part where the signal is active and a part where
# it is not. The techniques we'll be using in this tutorial depend on being
# able to contrast data that contains the signal of interest versus data that
meg_h5 = h5.File(downsamp_meg_file, 'r')
dset = meg_h5['/' + subj + '/MEG/' + meg_sess[0] + '/resampled_truncated']
meg_data = dset.value
meg_h5.close()
meg_timeseries[:, :, s] = meg_data
#Version where MEG filtering occurs before downsampling
# dset_name = database['/' + subj + '/MEG/' + meg_sess[0] + '/timeseries']
# meg_data = pu.read_database(dset_name, rois).values
# filt_data = pac.butter_filter(meg_data[:trunc_meg, :], 500, max_f, 'low')
# downsamp_data = resample(filt_data, int(meg_con))
# meg_timeseries[:, :, s] = downsamp_data
del fmri_data, meg_data
freq, coh = coherence(meg_timeseries[:, 0, 0], fmri_timeseries[:, 0, 0], fs=fs)
coh = coh - 1
n_iters = 1000
n = 0
coherence_perm = np.ndarray(shape=[n_iters, len(coh)])
while n != n_iters:
print('%s: Running permutation coherence %d' % (pu.ctime(), n + 1))
rand_subj = np.random.randint(0, len(subj_overlap))
rand_roi = np.random.randint(0, len(rois))
fmri_rand_ts = fmri_timeseries[:, rand_roi, rand_subj]
rand_subj = np.random.randint(0, len(subj_overlap))
rand_roi = np.random.randint(0, len(rois))
meg_rand_ts = meg_timeseries[:, rand_roi, rand_subj]
_, coh_perm = coherence(fmri_rand_ts, meg_rand_ts, fs=fs)
ax.set(xlabel='Time (s)', xlim=times[[0, -1]], ylabel='Amplitude (Am)',
title='Signal 1')
ax = axes[0][1]
ax.plot(times, 1e9 * signal2, lw=0.5)
ax.set(xlabel='Time (s)', xlim=times[[0, -1]], title='Signal 2')
# Power spectrum of the first timeseries
f, p = welch(signal1, fs=sfreq, nperseg=128, nfft=256)
ax = axes[1][0]
# Only plot the first 100 frequencies
ax.plot(f[:100], 20 * np.log10(p[:100]), lw=1.)
ax.set(xlabel='Frequency (Hz)', xlim=f[[0, 99]],
ylabel='Power (dB)', title='Power spectrum of signal 1')
# Compute the coherence between the two timeseries
f, coh = coherence(signal1, signal2, fs=sfreq, nperseg=100, noverlap=64)
ax = axes[1][1]
ax.plot(f[:50], coh[:50], lw=1.)
ax.set(xlabel='Frequency (Hz)', xlim=f[[0, 49]], ylabel='Coherence',
title='Coherence between the timeseries')
fig.tight_layout()
###############################################################################
# Now we put the signals at two locations on the cortex. We construct a
# :class:`mne.SourceEstimate` object to store them in.
#
# The timeseries will have a part where the signal is active and a part where
# it is not. The techniques we'll be using in this tutorial depend on being
# able to contrast data that contains the signal of interest versus data that
# does not (i.e. it contains only noise).
vmax=abs(cwtmatr).max(),
vmin=-abs(cwtmatr).max())
plt.show()
# %%
d = read_one_file('/home/tai/Desktop/results_stable.axa')
# %%
x, yf = drawfft(np.abs(np.array(d['Nx'])))
plt.plot(x, yf)
plt.xlim([-5, 5])
plt.ylim([-200, 200])
# %%
y = alll[0]['RVx']
x = alll[0]['RVy']
f, Cxy = signal.coherence(x, y, 100, nperseg=1024)
plt.semilogy(f, Cxy)
# %%
from sklearn.cross_decomposition import CCA
# %%
data = get_trajectory(name='Adam', seq=1)
X = data[0].iloc[:1000, :6]
Y = data[0].iloc[10000:11000, :6]
R = np.random.rand(1000, 6) - 1 / 2
#%%
X = (X - X.mean()) / X.std()
Y = (Y - Y.mean()) / Y.std()
print(X.shape)
def coh(self, mode):
t, b, e = self.get('t'), self.get('b' + mode), self.get('e' + mode)
return signal.coherence(b, e, fs=1/( t[1] - t[0] ), nperseg=t.size/2,
noverlap=t.size/2 - 1)[1]
def time_coherence(self):
signal.coherence(self.x, self.y)
def time_coherence(self):
signal.coherence(self.x, self.y)
def eig_centrality(X, fs=1000, connections=None, v0=None, tol=1e-3):
"""
Given a window of data, X, build a graph G with coherency as edges
and compute eigenvector centrality.
Parameters
----------
X: ndarray, shape(n,p)
data array of n samples, p channels
connections: list
list of either (i) integers
the integers are the channels that will become nodes
and the graph will be complete
or (ii) length 2 lists of integers
the integers correspond to directed edges
Returns
-------
eig_vec: ndarray, shape(p)
eigenvector of adjacency matrix
"""
# # build coherence graph
# if connections == None:
# n,p = X.shape
# connections = range(p)
# weightType = 'coherence'
# G = build_network(X, connections, weightType)
# # get the eigenvector centrality
# eig_dict = nx.eigenvector_centrality(G, weight='coherence')
# eig_vec = np.zeros(p)
# for i in range(p):
# eig_vec[i] = eig_dict[i]
# w = [1.0]
# get the data shape
n, p = X.shape
# initialize the adjcency matrix
A = np.zeros((p, p))
# construct adjacency matrix
for i in range(p):
for j in range(i + 1, p):
f, cxy = coherence(X[:, i], X[:, j], fs=fs)
# cxy, f = cohere(X[:,i], X[:,j], Fs=fs) # agggg using matplotlib because scipy is being dumb
c = np.mean(cxy)
A[i, j] = c # upper triangular part
A[j, i] = c # lower triangular part
if np.isnan(c):
print('(' + str(i) + ',' + str(j) + ") is nan")
# EDIT: none of these are working. They return NaN eigenvalues - why??
# print('Sums are: ', str(np.mean(A,axis=1)))
# Method 0: Power Iteration
maxiter = 12
tol = 1e-5
if v0 == None:
v0 = np.ones(p) / np.sqrt(p)
for i in range(maxiter):
# multiply and normalize
v_new = np.dot(A, v0)
v_new = v_new / np.linalg.norm(v_new)
# check for tolerance
diff = np.linalg.norm(v_new - v0)
if diff < tol:
break
# update iterate
v0 = v_new
v = v_new
w = np.array([np.mean(np.dot(A, v) / v)]) # eigenvalue
eig_vec = v
# # Method 1: All eigenvectors of symmetric matrix
# w,v = np.linalg.eigh(A, UPLO='U') # get the eigenvectors
# eig_vec = v[:,-1]
# # Method 2: Top 1 eigenvector of matrix
# w, v = scipy.sparse.linalg.eigs(A, k=1, v0=v0, tol=tol)
# eig_vec = v[:,0]x
# # Method 3: Top 1 eigenvector of a symmetric matrix
# w, v = scipy.sparse.linalg.eigsh(A, k=1, v0=v0, tol=tol)
# eig_vec = v[:,0]
return eig_vec
