def test_xmat(n):
"""test X_n = [[0, I], [I, 0]]"""
I = np.identity(n)
O = np.zeros_like(I)
X = np.block([[O, I], [I, O]])
res = Xmat(n)
assert np.all(X == res)
def test_numba_tor(N):
"""Tests numba implementations of the torontonian against the default implementation"""
cov = random_covariance(N)
O = Xmat(N) @ Amat(cov)
t1 = tor(O)
t2 = numba_tor(O)
t3 = rec_torontonian(O)
assert np.isclose(t1, t2)
assert np.isclose(t1, t3)
def test_numba_ltor(N):
"""Tests numba implementations of the loop torontonian against the default
implementation"""
alpha = np.random.random(N) + np.random.random(N) * 1j
alpha = np.concatenate((alpha, alpha.conj()))
cov = random_covariance(N)
O = Xmat(N) @ Amat(cov)
mu = O @ alpha
t1 = ltor(O, mu)
t2 = numba_ltor(O, mu)
t3 = rec_ltorontonian(O, mu)
assert np.isclose(t1, t2)
assert np.isclose(t1, t3)
def reference_count_unnormalized(cov, only_modes=None):
A = Amat(cov)
modes = cov.shape[0] // 2
if only_modes is not None:
mask = only_modes + tuple(x + modes for x in only_modes)
A = A[mask, :][:, mask]
xmat_size = len(only_modes)
else:
xmat_size = modes
O = Xmat(xmat_size) @ A
return tor(O).real
def Amat(self):
"""Constructs the A matrix from Hamilton's paper"""
######### this needs to be conjugated
sigmaq = np.concatenate(
(
np.concatenate((np.transpose(self.nmat), self.mmat), axis=1),
np.concatenate(
(np.transpose(np.conjugate(self.mmat)), self.nmat),
axis=1),
),
axis=0,
) + np.identity(2 * self.nlen)
return np.dot(Xmat(self.nlen),
np.identity(2 * self.nlen) - np.linalg.inv(sigmaq))
def test_Covmat():
""" Test the Covmat function by checking that its inverse function is Qmat """
n = 1
B = np.random.rand(n, n) + 1j * np.random.rand(n, n)
B = B + B.T
sc = find_scaling_adjacency_matrix(B, 1)
idm = np.identity(2 * n)
X = Xmat(n)
Bsc = sc * B
A = np.block([[Bsc, 0 * Bsc], [0 * Bsc, Bsc.conj()]])
Q = np.linalg.inv(idm - X @ A)
cov = Covmat(Q)
Qrec = Qmat(cov)
assert np.allclose(Q, Qrec)
def test_tor_and_threshold_displacement_prob_agree(n_modes):
"""Tests that threshold_detection_prob, ltor and the usual tor expression all agree
when displacements are zero"""
cv = random_covariance(n_modes)
mu = np.zeros([2 * n_modes])
Q = Qmat(cv)
O = Xmat(n_modes) @ Amat(cv)
expected = tor(O) / np.sqrt(np.linalg.det(Q))
prob = threshold_detection_prob(mu, cv, np.array([1] * n_modes))
prob2 = numba_ltor(O, mu) / np.sqrt(np.linalg.det(Q))
prob3 = rec_ltorontonian(O, mu) / np.sqrt(np.linalg.det(Q))
prob4 = numba_vac_prob(mu, Q) * ltor(O, mu)
assert np.isclose(expected, prob)
assert np.isclose(expected, prob2)
assert np.isclose(expected, prob3)
assert np.isclose(expected, prob4)