def test_lwr():
"test solution of lwr recursion"
for trial in xrange(3):
nc = np.random.randint(2, high=10)
P = np.random.randint(2, high=6)
# nc is channels, P is lags (order)
r = np.random.randn(P + 1, nc, nc)
r[0] = np.dot(r[0], r[0].T) # force r0 to be symmetric
a, Va = utils.lwr(r)
# Verify the "orthogonality" principle of the mAR system
# Set up a system in blocks to compute, for each k
# sum_{i=1}^{P} A(i)R(k-i) = -R(k) k > 0
# = sum_{i=1}^{P} R(k-i)^T A(i)^T = -R(k)^T
# = sum_{i=1}^{P} R(i-k)A(i)^T = -R(k)^T
rmat = np.zeros((nc * P, nc * P))
for k in xrange(1, P + 1):
for i in xrange(1, P + 1):
im = i - k
if im < 0:
r1 = r[-im].T
else:
r1 = r[im]
rmat[(k - 1) * nc : k * nc, (i - 1) * nc : i * nc] = r1
rvec = np.zeros((nc * P, nc))
avec = np.zeros((nc * P, nc))
for m in xrange(P):
rvec[m * nc : (m + 1) * nc] = -r[m + 1].T
avec[m * nc : (m + 1) * nc] = a[m].T
l2_d = np.dot(rmat, avec) - rvec
l2_d = (l2_d ** 2).sum() ** 0.5
l2_r = (rvec ** 2).sum() ** 0.5
# compute |Ax-b| / |b| metric
yield nt.assert_almost_equal, l2_d / l2_r, 0
# Rxx_11(k) is E{ z1(t)z1*(t-k) }
# So only Rxx(0) is symmetric
Rxx = np.empty((N,n_process,n_process,n_lags))
for i in xrange(N):
Rxx[i] = utils.autocov_vector(z[i],nlags=n_lags)
Rxx = Rxx.mean(axis=0)
R0 = Rxx[...,0]
Rm = Rxx[...,1:]
Rxx = Rxx.transpose(2,0,1)
a, ecov = utils.lwr(Rxx)
print 'compare coefficients to estimate:'
print a - am
print 'compare covariance to estimate:'
print ecov - cov
w, f_x2y, f_y2x, f_xy, Sw = alg.granger_causality_xy(a,ecov,Nfreqs=Nfreqs)
f = pp.figure()
c_x = np.empty((L,w.shape[0]))
c_y = np.empty((L,w.shape[0]))
for i in xrange(N):
frex,c_x[i],nu = alg.multi_taper_psd(z[i][0])
frex,c_y[i],nu = alg.multi_taper_psd(z[i][1])
