def corr3(x1, x2=None, window=50):
"""
x1 and x2 are binned spikes.
"""
if x2 is None:
x2 = x1
corr = np.zeros((window * 2 + 1))
# Positive lag
corr[:window + 1] = pycorrelate.ucorrelate(x1, x2, window + 1)[::-1]
# Negative lag
corr[window:] = pycorrelate.ucorrelate(x2, x1, window + 1)
return corr
def test_ucorrelate(data):
"""Test ucorrelate against np.correlate."""
t, u, unit = data
binwidth = 50e-6
bins_tt = np.arange(0, t.max() * unit, binwidth) / unit
bins_uu = np.arange(0, u.max() * unit, binwidth) / unit
tx, _ = np.histogram(t, bins=bins_tt)
ux, _ = np.histogram(u, bins=bins_uu)
C = np.correlate(ux, tx, mode='full')
Gn = C[tx.size - 1:] # trim to positive time lags
Gu = pyc.ucorrelate(tx, ux)
assert (Gu == Gn).all()
Gu2 = pyc.ucorrelate(tx, ux, maxlag=1000)
assert (Gu2 == Gn[:1000]).all()
def allcorr2(allspikes, window):
pxc = np.zeros((n, n, window))
for i in range(n):
for j in range(n):
if i >= j:
pxc[i, j, :] = pycorrelate.ucorrelate(allspikes[i, :],
allspikes[j, :], window)
def cross_corr(a, b): #max up/down shift N = 5 #returns peak value and offset for the cross-correlation of a and b # res = np.correlate( a, b, mode="same") # offset = np.argmax(res) - len(res)//2 #this is working and equivalent, but not significantly faster than the full numpy cross-correlation res = np.empty(N*2+1) #can't do negative lag so just shift them and piece both together first = pyc.ucorrelate(a, b, maxlag=N+1) second = pyc.ucorrelate(b, a, maxlag=N+1) res[:N+1] = first[::-1] res[N+1:] = second[1:] offset = np.argmax(res)-N # this is not equivalent # for i, x in enumerate(range(-N, N+1)): # # out[i] = np.sum(np.abs(a- np.roll(b, x) )) # out[i] = np.correlate( a, np.roll(b, x), mode="valid") return offset
def test_pcorrelate_vs_ucorrelate(data):
t, u, unit = data
binwidth = 50e-6
bins_tt = np.arange(0, t.max() * unit, binwidth) / unit
bins_uu = np.arange(0, u.max() * unit, binwidth) / unit
tx, _ = np.histogram(t, bins=bins_tt)
ux, _ = np.histogram(u, bins=bins_uu)
Gu = pyc.ucorrelate(tx, ux)
maxlag_sec = 1.2 # seconds
lagbins = (np.arange(0, maxlag_sec, binwidth) / unit).astype('int64')
Gp = pyc.pcorrelate(t, u, lagbins) * int(binwidth / unit)
n = 6000
err = np.abs(Gp[:n] - Gu[:n]) / (0.5 * (Gp[:n] + Gu[:n]))
assert err.max() < 0.23
assert err.mean() < 0.05
def cross_correlation_using_all_approaches_with_instrumentation(
signal_x=[], signal_y=[]):
# List of tuples storing results regarding cross-correlation.
results = []
"""
Enumerate all modes of NumPy's correlate function.
In the example from \cite{TheSciPyCommunity2019},
the cross-correlation has values greater than 1;
since the notes in \cite{TheSciPyCommunity2019}
indicate that the definition for
cross-correlation "is not unique," this can
explain why the cross-correlation for the
"valid" mode is >1.
"""
for current_mode in approx_cross_correlation.numpy_correlate_modes:
prompt = " ... Testing NumPy-based cross-correlation's " + current_mode + " mode. {}"
statistical_analysis.increment_number_test_cases_used()
# Determine the cross-correlation using the current mode.
cross_correlation_from_numpy_correlate = approx_cross_correlation.cross_correlation_using_numpy(
signal_x, signal_y, current_mode)
#print("NumPy-based cross-correlation using",current_mode,"mode is:",cross_correlation_from_numpy_correlate,"=")
"""
Perform statistical analysis on the set of
cross-correlation values.
"""
std_dev_cross_correlation = np.std(
cross_correlation_from_numpy_correlate)
#print(" NumPy-based cross-correlation's standard deviation using",current_mode,"mode is:",std_dev_cross_correlation,"=")
var_cross_correlation = np.var(
cross_correlation_from_numpy_correlate)
#print(" NumPy-based cross-correlation's variance using",current_mode,"mode is:",var_cross_correlation,"=")
arith_mean_cross_correlation = np.mean(
cross_correlation_from_numpy_correlate)
#print(" NumPy-based cross-correlation's arithmetic mean using",current_mode,"mode is:",arith_mean_cross_correlation,"=")
ptp_cross_correlation = np.ptp(
cross_correlation_from_numpy_correlate)
#print(" NumPy-based cross-correlation's min and max values (or peak to peak) using",current_mode,"mode is:",ptp_cross_correlation,"=")
amax_cross_correlation = np.amax(
cross_correlation_from_numpy_correlate)
#print(" NumPy-based cross-correlation's max value using",current_mode,"mode is:",amax_cross_correlation,"=")
amin_cross_correlation = np.amin(
cross_correlation_from_numpy_correlate)
#print(" NumPy-based cross-correlation's min value using",current_mode,"mode is:",amin_cross_correlation,"=")
#print("")
results.append(
(current_mode, cross_correlation_from_numpy_correlate,
std_dev_cross_correlation, var_cross_correlation,
arith_mean_cross_correlation, ptp_cross_correlation,
amax_cross_correlation, amin_cross_correlation))
print(prompt.format("OK"))
statistical_analysis.increment_number_test_cases_passed()
"""
Matplotlib.pyplot's solution for correlation causes
execution error
(lags, c, line, b) = plt.xcorr(signal_x, signal_y,maxlags=4)
print("Matplotlib.pyplot lags",lags,"=")
print("Matplotlib.pyplot c",c,"=")
print("Matplotlib.pyplot line",line,"=")
print("Matplotlib.pyplot b",b,"=")
"""
cross_correlation_from_pycorrelate = pyc.ucorrelate(
np.array(signal_x), np.array(signal_y))
#print("Pycorrelate-based cross-correlation is:",cross_correlation_from_pycorrelate,"=")
"""
Perform statistical analysis on the set of
cross-correlation values.
"""
std_dev_cross_correlation = np.std(cross_correlation_from_pycorrelate)
print(" NumPy-based cross-correlation's standard deviation using",
current_mode, "mode is:", std_dev_cross_correlation, "=")
var_cross_correlation = np.var(cross_correlation_from_pycorrelate)
print(" NumPy-based cross-correlation's variance using", current_mode,
"mode is:", var_cross_correlation, "=")
arith_mean_cross_correlation = np.mean(
cross_correlation_from_pycorrelate)
print(" NumPy-based cross-correlation's arithmetic mean using",
current_mode, "mode is:", arith_mean_cross_correlation, "=")
ptp_cross_correlation = np.ptp(cross_correlation_from_pycorrelate)
print(
" NumPy-based cross-correlation's min and max values (or peak to peak) using",
current_mode, "mode is:", ptp_cross_correlation, "=")
amax_cross_correlation = np.amax(cross_correlation_from_pycorrelate)
print(" NumPy-based cross-correlation's max value using", current_mode,
"mode is:", amax_cross_correlation, "=")
amin_cross_correlation = np.amin(cross_correlation_from_pycorrelate)
print(" NumPy-based cross-correlation's min value using", current_mode,
"mode is:", amin_cross_correlation, "=")
print("")
results.append(("pyc.ucorrelate", cross_correlation_from_pycorrelate,
std_dev_cross_correlation, var_cross_correlation,
arith_mean_cross_correlation, ptp_cross_correlation,
amax_cross_correlation, amin_cross_correlation))
return results
x, y = cell_storm_opt.data.data_dict['storm'][
'x'], cell_storm_opt.data.data_dict['storm']['y']
perimeter = cell_storm_opt.coords.calc_perimeter(x, y)
# Sampling points
x_out = np.linspace(0, cell_storm_opt.circumference, num=20000, endpoint=True)
dx = np.diff(x_out)[0]
# Sum convolution with gaussian
y_out = running_sum(np.sort(perimeter),
np.ones_like(perimeter),
x_out,
sigma=0.075)
# Autocorrelation
G = ucorrelate(y_out, y_out)
# Remove low-frequency component
G_m = uniform_filter1d(G, size=200)
acf = G - G_m
#https://stackoverflow.com/questions/11205037/detect-period-of-unknown-source
fourier = np.fft.fft(acf) / len(acf)
n = acf.size
freq = np.fft.fftfreq(n, d=dx)
sns.set_style('ticks')
ax_loc = plt.subplot(bot_grid[0])
ax_loc.plot(x_out * (80 / 1000), y_out)
ax_loc.set_xlim(0, np.max(x_out) * (80 / 1000))
ax_loc.set_ylabel('Localizations')