def test_spherical_commutator(self):
# Define Spin Basis Operators
s0 = la.SphericalSpinOperator((0, 0, 0, 0))
si = la.SphericalSpinOperator((1, 0, 0, 0))
sx = la.SphericalSpinOperator((0, 1, np.pi / 2, 0))
sy = la.SphericalSpinOperator((0, 1, np.pi / 2, np.pi / 2))
sz = la.SphericalSpinOperator((0, 1, 0, 0))
self.assertEqual(s0, la.commutator(si, sx))
self.assertEqual(la.commutator(sx, sy), -1 * la.commutator(sy, sx))
self.assertEqual(2j * sz, la.commutator(sx, sy))
def setUp(self):
self.i = (1., 0., 0., 0.)
self.x = (0., 1., np.pi / 2, 0.)
self.y = (0., 1., np.pi / 2, np.pi / 2)
self.z = (0., 1., 0., 0.)
self.si = la.SphericalSpinOperator(self.i)
self.sx = la.SphericalSpinOperator(self.x)
self.sy = la.SphericalSpinOperator(self.y)
self.sz = la.SphericalSpinOperator(self.z)
pass
def test_vector_grid_init_from_spherical_operator_mesh(self):
ops = []
for xx in r:
for yy in t:
for zz in p:
ops.append(la.SphericalSpinOperator((0, xx, yy, zz)))
ops = np.reshape(ops, s_grid.shape)
vector_grid = gr.VectorGrid(ops, s_grid)
self.assertIs(vector_grid._operator_type, la.SphericalSpinOperator)
self.assertIs(vector_grid._container_type, tuple)
self.assertEqual(vector_grid._operator_dim, 4)
self.assertTrue(np.array_equal(ops, vector_grid.data))
self.assertEqual(vector_grid[0, 0, 0], (la.SphericalSpinOperator(
(0, 0, 0, 0)), (0, 0, 0)))
def test_vector_grid_init_from_spherical_coordinate_mesh(self):
ops_e = []
for xx in r:
for yy in t:
for zz in p:
ops_e.append(la.SphericalSpinOperator((0, xx, yy, zz)))
ops_e = np.reshape(ops_e, s_grid.shape)
vector_grid = gr.VectorGrid(list(s_grid.mesh),
s_grid,
operator_type=la.SphericalSpinOperator)
self.assertIs(vector_grid._operator_type, la.SphericalSpinOperator)
self.assertIs(vector_grid._container_type, list)
self.assertEqual(vector_grid._operator_dim, 4)
self.assertTrue(np.array_equal(ops_e, vector_grid.data))
self.assertEqual(vector_grid[0, 0, 0], (la.SphericalSpinOperator(
(0, 0, 0, 0)), (0, 0, 0)))
def test_mixed_commutator(self):
# Define Spin Basis Operators
s0c = la.CartesianSpinOperator((0, 0, 0, 0))
sic = la.CartesianSpinOperator((1, 0, 0, 0))
sxc = la.CartesianSpinOperator((0, 1, 0, 0))
syc = la.CartesianSpinOperator((0, 0, 1, 0))
szc = la.CartesianSpinOperator((0, 0, 0, 1))
# Define Spin Basis Operators
s0s = la.SphericalSpinOperator((0, 0, 0, 0))
sis = la.SphericalSpinOperator((1, 0, 0, 0))
sxs = la.SphericalSpinOperator((0, 1, np.pi / 2, 0))
sys = la.SphericalSpinOperator((0, 1, np.pi / 2, np.pi / 2))
szs = la.SphericalSpinOperator((0, 1, 0, 0))
self.assertAlmostEqual(s0c, la.commutator(sis, sxc))
self.assertAlmostEqual(la.commutator(sxs, syc),
-1 * la.commutator(sys, sxc))
self.assertAlmostEqual(2j * szs, la.commutator(sxc, sys))
def test_vectorize_spherical(self):
si = la.SphericalSpinOperator((1, 0, 0, 0))
sx = la.SphericalSpinOperator((0, 1, pi / 2, 0))
sy = la.SphericalSpinOperator((0, 1, pi / 2, pi / 2))
sz = la.SphericalSpinOperator((0, 1, 0, 0))
ops = np.array([[si, sx], [sy, sz]])
expected = (np.array([[1, 0], [0, 0]]), np.array([[0, 1], [0, 0]]),
np.array([[0, 0], [1, 0]]), np.array([[0, 0], [0, 1]]))
x1 = (0, 1)
x2 = (0, 1)
grid = gr.CartesianGrid((x1, x2))
op_grid = gr.GridData(ops, grid)
expected = gr.GridData(expected, grid)
calculated = gr.vectorize_operator_grid(op_grid)
self.assertAlmostEqual(expected, calculated)
def test_vector_grid_cartesian_vectors(self):
ops = []
for xx in r:
for yy in t:
for zz in p:
ops.append(la.SphericalSpinOperator((0, xx, yy, zz)))
ops = np.reshape(ops, s_grid.shape)
vector_grid = gr.VectorGrid(ops, s_grid)
vectors = vector_grid.cartesian_vectors
self.assertTrue(np.array_equal(vectors, s_grid.cartesian))
def test_spherical_gradient(self):
funct = s_grid.mesh[0]
data_grid = gr.DataGrid(funct, s_grid)
ops = []
for xx in r:
for yy in t:
for zz in p:
ops.append(la.SphericalSpinOperator((0, 1, 0, 0)))
ops = np.reshape(ops, s_grid.shape)
vector_grid = gr.VectorGrid(ops, s_grid)
self.assertAlmostEqual(
vector_grid, data_grid.gradient(la.SphericalSpinOperator, tuple))
def test_nonzero_unitary_dynamics_mixed_spin_operator(self):
rhox = la.CartesianSpinOperator((0.5, 0.5, 0., 0.))
rhoy = la.CartesianSpinOperator((0.5, 0., 0.5, 0.))
rhoxy = la.CartesianSpinOperator((0.5, 0.5, 0.5, 0.))
rhoxdot_expected = la.CartesianSpinOperator((0., 0., 1., 0.))
rhoydot_expected = la.CartesianSpinOperator((0., -1., 0., 0.))
rhoxydot_expected = la.CartesianSpinOperator((0., -1., 1., 0.))
ham = la.SphericalSpinOperator((0, 1, 0, 0))
rhoxdot_calc = hbar * unitary_derivative(rhox, ham)
rhoydot_calc = hbar * unitary_derivative(rhoy, ham)
rhoxydot_calc = hbar * unitary_derivative(rhoxy, ham)
self.assertAlmostEqual(rhoxdot_calc, rhoxdot_expected)
self.assertAlmostEqual(rhoydot_calc, rhoydot_expected)
self.assertAlmostEqual(rhoxydot_calc, rhoxydot_expected)
def test_nonzero_unitary_dynamics_spherical_spin_operator(self):
rhox = la.SphericalSpinOperator((0.5, 0.5, np.pi/2, 0.))
rhoy = la.SphericalSpinOperator((0.5, 0.5, np.pi/2, np.pi/2))
rhoxy = la.SphericalSpinOperator((0.5, 0.5, np.pi/2, np.pi/4))
rhoxdot_expected = 1 / hbar * la.SphericalSpinOperator((0., 1., np.pi/2, np.pi/2))
rhoydot_expected = 1 / hbar * la.SphericalSpinOperator((0., 1., np.pi/2, np.pi))
rhoxydot_expected = 1 / hbar * la.SphericalSpinOperator((0., 1., np.pi/2, 3*np.pi/4))
ham = la.SphericalSpinOperator((0, 1, 0, 0))
rhoxdot_calc = unitary_derivative(rhox, ham)
rhoydot_calc = unitary_derivative(rhoy, ham)
rhoxydot_calc = unitary_derivative(rhoxy, ham)
self.assertEqual(rhoxdot_calc, rhoxdot_expected)
self.assertEqual(rhoydot_calc, rhoydot_expected)
self.assertEqual(rhoxydot_calc, rhoxydot_expected)
def test_steady_state_unitary_dynamics_mixed_spin_operator(self):
rho0 = la.SphericalSpinOperator((1 / 2, 0, 0, 0))
rhodot_expected = la.SphericalSpinOperator((0, 0, 0, 0))
ham = la.CartesianSpinOperator((0, 0, 0, 1))
self.assertEqual(unitary_derivative(rho0, ham), rhodot_expected)
def test_init_length_assertion(self):
""" Tests that the constructor correctly raises initialization error if the wrong length input provided """
with self.assertRaises(AssertionError):
la.SphericalSpinOperator((1., 0., 0.))
with self.assertRaises(AssertionError):
la.SphericalSpinOperator((1., 0., 0., 0., 0., 0.))