def testPhase(self):
"""Check that the Hopf map is invariant under multiplication
by a random phase."""
X = hopf(self.psi)
theta = random_vector(self.N) # Column vector of phases
phase = hstack(np.exp(1j*theta), 2)
self.assertTrue(is_float_equal(X, hopf(phase*self.psi)))
def testInverse(self):
"""Check that Hopf map composed with its inverse yield the identity."""
# Hopf composed with the inverse should give the identity exactly
X1 = hopf(inverse_hopf(self.X))
self.assertTrue(is_float_equal(X1, self.X))
# Inverse hopf composed with Hopf gives the identity up to phase
psi1 = inverse_hopf(hopf(self.psi))
phases = psi1/self.psi
# Test whether columns of phase matrix are equal
self.assertTrue(is_float_equal(phases[:, 0], phases[:, 1]))
# Test whether column elements have unit norm
p = phases[:, 0]
self.assertTrue(is_float_equal(p*p.conjugate(), np.ones(self.N)))