def test_AR_LD():
"""
Test the Levinson Durbin estimate of the AR coefficients against the
expercted PSD
"""
arsig,_,_ = utils.ar_generator(N=512)
avg_pwr = (arsig*arsig.conjugate()).real.mean()
order = 8
ak, sigma_v = tsa.AR_est_LD(arsig, order)
w, psd = tsa.AR_psd(ak, sigma_v)
# the psd is a one-sided power spectral density, which has been
# multiplied by 2 to preserve the property that
# 1/2pi int_{-pi}^{pi} Sxx(w) dw = Rxx(0)
# evaluate this integral numerically from 0 to pi
dw = np.pi/len(psd)
avg_pwr_est = np.trapz(psd, dx=dw) / (2*np.pi)
npt.assert_almost_equal(avg_pwr, avg_pwr_est, decimal=0)
# Test for providing the autocovariance as an input:
ak,sigma_v = tsa.AR_est_LD(arsig, order, utils.autocov(arsig))
w, psd = tsa.AR_psd(ak, sigma_v)
avg_pwr_est = np.trapz(psd, dx=dw) / (2*np.pi)
npt.assert_almost_equal(avg_pwr, avg_pwr_est, decimal=0)
def test_AR_LD():
"""
Test the Levinson Durbin estimate of the AR coefficients against the
expercted PSD
"""
arsig, _, _ = utils.ar_generator(N=512)
avg_pwr = (arsig * arsig.conjugate()).real.mean()
order = 8
ak, sigma_v = tsa.AR_est_LD(arsig, order)
w, psd = tsa.AR_psd(ak, sigma_v)
# the psd is a one-sided power spectral density, which has been
# multiplied by 2 to preserve the property that
# 1/2pi int_{-pi}^{pi} Sxx(w) dw = Rxx(0)
# evaluate this integral numerically from 0 to pi
dw = np.pi / len(psd)
avg_pwr_est = np.trapz(psd, dx=dw) / (2 * np.pi)
npt.assert_almost_equal(avg_pwr, avg_pwr_est, decimal=0)
# Test for providing the autocovariance as an input:
ak, sigma_v = tsa.AR_est_LD(arsig, order, utils.autocov(arsig))
w, psd = tsa.AR_psd(ak, sigma_v)
avg_pwr_est = np.trapz(psd, dx=dw) / (2 * np.pi)
npt.assert_almost_equal(avg_pwr, avg_pwr_est, decimal=0)
def _plot_acov_fired(self):
t, y = self.curve_manager.interactive_curve.current_data(
full_xdata=False)
y *= 1e6
t_stamp = t.mean()
t = (t - t[0]) * 1e3
dt = t[1] - t[0]
N = int(self.n_lags / dt)
Ct = autocov(y, all_lags=False)[:, :min(len(t), N)]
if self.norm_kernel:
Ct /= Ct[:, 0][:, None]
chan_map = self.chan_map
frames = chan_map.embed(Ct.T, axis=1)
fig = Figure(figsize=(6, 10))
ax1 = subplot2grid(fig, (2, 1), (0, 0))
ax2 = subplot2grid(fig, (2, 1), (1, 0))
# top panel is acov map at lag t
mx = np.abs(Ct).max()
_, cb = chan_map.image(Ct[:, 0], cmap='bwr', clim=(-mx, mx), ax=ax1)
ax1.set_title('Map of ~ t={0:.2f} sec'.format(t_stamp))
# bottom panel left: acov as function of lag t
ax2.plot(t[:len(frames)], Ct.T, lw=.25, color='k')
ax2.set_xlabel('Lags (ms)')
if self.norm_kernel:
ax1.set_title('Map of autocorr. ~ t={0:.2f} sec'.format(t_stamp))
cb.set_label('Autocorrelation')
ax2.set_ylabel('Autocorrelation')
else:
ax1.set_title('Map of autocov. ~ t={0:.2f} sec'.format(t_stamp))
cb.set_label('Autocovariance')
ax2.set_ylabel('Autocovariance')
plotters.sns.despine(ax=ax2)
splot = MultiframeSavesFigure(fig,
frames,
mode_name='lag (ms)',
frame_index=t[:len(frames)])
splot.edit_traits()
fig.tight_layout()
fig.canvas.draw_idle()
if not hasattr(self, '_kernel_plots'):
self._kernel_plots = [splot]
else:
self._kernel_plots.append(splot)
def test_AR_YW():
arsig,_,_ = utils.ar_generator(N=512)
avg_pwr = (arsig*arsig.conjugate()).mean()
order = 8
ak,sigma_v = tsa.AR_est_YW(arsig, order)
w, psd = tsa.AR_psd(ak, sigma_v)
# the psd is a one-sided power spectral density, which has been
# multiplied by 2 to preserve the property that
# 1/2pi int_{-pi}^{pi} Sxx(w) dw = Rxx(0)
# evaluate this integral numerically from 0 to pi
dw = np.pi / len(psd)
avg_pwr_est = np.trapz(psd, dx=dw) / (2*np.pi)
# consistency on the order of 10**0 is pretty good for this test
npt.assert_almost_equal(avg_pwr, avg_pwr_est, decimal=0)
# Test for providing the autocovariance as an input:
ak,sigma_v = tsa.AR_est_YW(arsig, order, utils.autocov(arsig))
w, psd = tsa.AR_psd(ak, sigma_v)
avg_pwr_est = np.trapz(psd, dx=dw) / (2*np.pi)
npt.assert_almost_equal(avg_pwr, avg_pwr_est, decimal=0)
def test_AR_YW():
arsig, _, _ = utils.ar_generator(N=512)
avg_pwr = (arsig * arsig.conjugate()).mean()
order = 8
ak, sigma_v = tsa.AR_est_YW(arsig, order)
w, psd = tsa.AR_psd(ak, sigma_v)
# the psd is a one-sided power spectral density, which has been
# multiplied by 2 to preserve the property that
# 1/2pi int_{-pi}^{pi} Sxx(w) dw = Rxx(0)
# evaluate this integral numerically from 0 to pi
dw = np.pi / len(psd)
avg_pwr_est = np.trapz(psd, dx=dw) / (2 * np.pi)
# consistency on the order of 10**0 is pretty good for this test
npt.assert_almost_equal(avg_pwr, avg_pwr_est, decimal=0)
# Test for providing the autocovariance as an input:
ak, sigma_v = tsa.AR_est_YW(arsig, order, utils.autocov(arsig))
w, psd = tsa.AR_psd(ak, sigma_v)
avg_pwr_est = np.trapz(psd, dx=dw) / (2 * np.pi)
npt.assert_almost_equal(avg_pwr, avg_pwr_est, decimal=0)
