def test_dot_HS(self):
U, V = rng.randint(0, 100, (2, 2, 2))
S = util.dot_HS(U, V)
T = util.dot_HS(U, V, eps=0)
self.assertArrayEqual(S, T)
for d in rng.randint(2, 10, (5, )):
U, V = testutil.rand_herm(d, 2)
self.assertArrayAlmostEqual(util.dot_HS(U, V),
(U.conj().T @ V).trace())
U = testutil.rand_unit(d).squeeze()
self.assertEqual(util.dot_HS(U, U), d)
self.assertEqual(util.dot_HS(U, U + 1e-14, eps=1e-10), d)
def test_oper_equiv(self):
with self.assertRaises(ValueError):
util.oper_equiv(rng.standard_normal((2, 2)),
rng.standard_normal((3, 3)))
for d in rng.randint(2, 10, (5, )):
psi = rng.standard_normal((d, 1)) + 1j * rng.standard_normal(
(d, 1))
# Also test broadcasting
U = testutil.rand_herm(d, rng.randint(1, 11)).squeeze()
phase = rng.standard_normal()
result = util.oper_equiv(psi, psi * np.exp(1j * phase))
self.assertTrue(result[0])
self.assertAlmostEqual(result[1], phase, places=5)
result = util.oper_equiv(psi * np.exp(1j * phase), psi)
self.assertTrue(result[0])
self.assertAlmostEqual(result[1], -phase, places=5)
psi /= np.linalg.norm(psi, ord=2)
result = util.oper_equiv(psi,
psi * np.exp(1j * phase),
normalized=True,
eps=1e-13)
self.assertTrue(result[0])
self.assertArrayAlmostEqual(result[1], phase, atol=1e-5)
result = util.oper_equiv(psi, psi + 1)
self.assertFalse(result[0])
result = util.oper_equiv(U, U * np.exp(1j * phase))
self.assertTrue(np.all(result[0]))
self.assertArrayAlmostEqual(result[1], phase, atol=1e-5)
result = util.oper_equiv(U * np.exp(1j * phase), U)
self.assertTrue(np.all(result[0]))
self.assertArrayAlmostEqual(result[1], -phase, atol=1e-5)
norm = np.sqrt(util.dot_HS(U, U))
norm = norm[:, None, None] if U.ndim == 3 else norm
U /= norm
# TIP: In numpy 1.18 we could just do:
# U /= np.expand_dims(np.sqrt(util.dot_HS(U, U)), axis=(-1, -2))
result = util.oper_equiv(U,
U * np.exp(1j * phase),
normalized=True,
eps=1e-10)
self.assertTrue(np.all(result[0]))
self.assertArrayAlmostEqual(result[1], phase)
result = util.oper_equiv(U, U + 1)
self.assertFalse(np.all(result[0]))
def test_oper_equiv(self):
with self.assertRaises(ValueError):
util.oper_equiv(*[np.ones((1, 2, 3))] * 2)
for d in rng.randint(2, 10, (5, )):
psi = rng.standard_normal((d, 1)) + 1j * rng.standard_normal(
(d, 1))
U = testutil.rand_herm(d).squeeze()
phase = rng.standard_normal()
result = util.oper_equiv(psi, psi * np.exp(1j * phase))
self.assertTrue(result[0])
self.assertAlmostEqual(result[1], phase, places=5)
result = util.oper_equiv(psi * np.exp(1j * phase), psi)
self.assertTrue(result[0])
self.assertAlmostEqual(result[1], -phase, places=5)
psi /= np.linalg.norm(psi, ord=2)
result = util.oper_equiv(psi,
psi * np.exp(1j * phase),
normalized=True,
eps=1e-13)
self.assertTrue(result[0])
self.assertAlmostEqual(result[1], phase, places=5)
result = util.oper_equiv(psi, psi + 1)
self.assertFalse(result[0])
result = util.oper_equiv(U, U * np.exp(1j * phase))
self.assertTrue(result[0])
self.assertAlmostEqual(result[1], phase, places=5)
result = util.oper_equiv(U * np.exp(1j * phase), U)
self.assertTrue(result[0])
self.assertAlmostEqual(result[1], -phase, places=5)
U /= np.sqrt(util.dot_HS(U, U))
result = util.oper_equiv(U,
U * np.exp(1j * phase),
normalized=True,
eps=1e-10)
self.assertTrue(result[0])
self.assertAlmostEqual(result[1], phase)
result = util.oper_equiv(U, U + 1)
self.assertFalse(result[0])
def test_dot_HS(self):
for d in rng.randint(2, 10, (5, )):
U = qutip.rand_herm(d)
V = qutip.rand_herm(d)
self.assertArrayAlmostEqual(util.dot_HS(U, V), (U.dag() * V).tr())
U = qutip.rand_unitary(d)
self.assertEqual(util.dot_HS(U, U), d)
self.assertEqual(util.dot_HS(U, U + 1e-14, eps=1e-10), d)
self.assertArrayAlmostEqual(util.dot_HS(U, V), (U.dag() * V).tr())
U = qutip.rand_unitary(d)
self.assertEqual(util.dot_HS(U, U), d)
self.assertEqual(util.dot_HS(U, U + 1e-14, eps=1e-10), d)
