def test_MAR_est_LWR():
"""
Test the LWR MAR estimator against the power of the signal
This also tests the functions: transfer_function_xy, spectral_matrix_xy,
coherence_from_spectral and granger_causality_xy
"""
# This is the same processes as those in doc/examples/ar_est_2vars.py:
a1 = np.array([ [0.9, 0],
[0.16, 0.8] ])
a2 = np.array([ [-0.5, 0],
[-0.2, -0.5] ])
am = np.array([ -a1, -a2 ])
x_var = 1
y_var = 0.7
xy_cov = 0.4
cov = np.array([ [x_var, xy_cov],
[xy_cov, y_var] ])
n_freqs = 1024
w, Hw = tsa.transfer_function_xy(am, n_freqs=n_freqs)
Sw = tsa.spectral_matrix_xy(Hw, cov)
# This many realizations of the process:
N = 500
# Each one this long
L = 1024
order = am.shape[0]
n_lags = order + 1
n_process = am.shape[-1]
z = np.empty((N, n_process, L))
nz = np.empty((N, n_process, L))
for i in xrange(N):
z[i], nz[i] = utils.generate_mar(am, cov, L)
a_est = []
cov_est = []
# This loop runs MAR_est_LWR:
for i in xrange(N):
Rxx = (tsa.MAR_est_LWR(z[i],order=n_lags))
a_est.append(Rxx[0])
cov_est.append(Rxx[1])
a_est = np.mean(a_est,0)
cov_est = np.mean(cov_est,0)
# This tests transfer_function_xy and spectral_matrix_xy:
w, Hw_est = tsa.transfer_function_xy(a_est, n_freqs=n_freqs)
Sw_est = tsa.spectral_matrix_xy(Hw_est, cov_est)
# coherence_from_spectral:
c = tsa.coherence_from_spectral(Sw)
c_est = tsa.coherence_from_spectral(Sw_est)
# granger_causality_xy:
w, f_x2y, f_y2x, f_xy, Sw = tsa.granger_causality_xy(am,
cov,
n_freqs=n_freqs)
w, f_x2y_est, f_y2x_est, f_xy_est, Sw_est = tsa.granger_causality_xy(a_est,
cov_est,
n_freqs=n_freqs)
# interdependence_xy
i_xy = tsa.interdependence_xy(Sw)
i_xy_est = tsa.interdependence_xy(Sw_est)
# This is all very approximate:
npt.assert_almost_equal(Hw,Hw_est,decimal=1)
npt.assert_almost_equal(Sw,Sw_est,decimal=1)
npt.assert_almost_equal(c,c_est,1)
npt.assert_almost_equal(f_xy,f_xy_est,1)
npt.assert_almost_equal(f_x2y,f_x2y_est,1)
npt.assert_almost_equal(f_y2x,f_y2x_est,1)
npt.assert_almost_equal(i_xy,i_xy_est,1)
Finally, we calculate the total causality, which is the sum of all the above
causalities. We compare this to the interdependence between the processes. This is the
measure of total dependence and is closely akin to the coherence between the
processes. We also compare to the empirically calculated coherence:
"""
fig03 = plt.figure()
ax03 = fig03.add_subplot(1, 1, 1)
# total causality
ax03.plot(w, f_xy + f_x2y + f_y2x, label='Total causality')
#Interdepence:
f_id = alg.interdependence_xy(Sw)
ax03.plot(w, f_id, label='Interdependence')
coh = np.empty((N, 33))
for i in range(N):
frex, this_coh = alg.coherence(z[i])
coh[i] = this_coh[0, 1]
ax03.plot(frex, np.mean(coh, axis=0), label='Coherence')
ax03.legend()
"""
.. image:: fig/ar_est_2vars_03.png
def test_MAR_est_LWR():
"""
Test the LWR MAR estimator against the power of the signal
This also tests the functions: transfer_function_xy, spectral_matrix_xy,
coherence_from_spectral and granger_causality_xy
"""
# This is the same processes as those in doc/examples/ar_est_2vars.py:
a1 = np.array([[0.9, 0], [0.16, 0.8]])
a2 = np.array([[-0.5, 0], [-0.2, -0.5]])
am = np.array([-a1, -a2])
x_var = 1
y_var = 0.7
xy_cov = 0.4
cov = np.array([[x_var, xy_cov], [xy_cov, y_var]])
n_freqs = 1024
w, Hw = tsa.transfer_function_xy(am, n_freqs=n_freqs)
Sw = tsa.spectral_matrix_xy(Hw, cov)
# This many realizations of the process:
N = 500
# Each one this long
L = 1024
order = am.shape[0]
n_lags = order + 1
n_process = am.shape[-1]
z = np.empty((N, n_process, L))
nz = np.empty((N, n_process, L))
for i in range(N):
z[i], nz[i] = utils.generate_mar(am, cov, L)
a_est = []
cov_est = []
# This loop runs MAR_est_LWR:
for i in range(N):
Rxx = (tsa.MAR_est_LWR(z[i], order=n_lags))
a_est.append(Rxx[0])
cov_est.append(Rxx[1])
a_est = np.mean(a_est, 0)
cov_est = np.mean(cov_est, 0)
# This tests transfer_function_xy and spectral_matrix_xy:
w, Hw_est = tsa.transfer_function_xy(a_est, n_freqs=n_freqs)
Sw_est = tsa.spectral_matrix_xy(Hw_est, cov_est)
# coherence_from_spectral:
c = tsa.coherence_from_spectral(Sw)
c_est = tsa.coherence_from_spectral(Sw_est)
# granger_causality_xy:
w, f_x2y, f_y2x, f_xy, Sw = tsa.granger_causality_xy(am,
cov,
n_freqs=n_freqs)
w, f_x2y_est, f_y2x_est, f_xy_est, Sw_est = tsa.granger_causality_xy(
a_est, cov_est, n_freqs=n_freqs)
# interdependence_xy
i_xy = tsa.interdependence_xy(Sw)
i_xy_est = tsa.interdependence_xy(Sw_est)
# This is all very approximate:
npt.assert_almost_equal(Hw, Hw_est, decimal=1)
npt.assert_almost_equal(Sw, Sw_est, decimal=1)
npt.assert_almost_equal(c, c_est, 1)
npt.assert_almost_equal(f_xy, f_xy_est, 1)
npt.assert_almost_equal(f_x2y, f_x2y_est, 1)
npt.assert_almost_equal(f_y2x, f_y2x_est, 1)
npt.assert_almost_equal(i_xy, i_xy_est, 1)
