def test_random_two_wedge_two():
"""
Test wedge product code with a random 4-tensor and a random 4-tensor
(a, b, h, g) wedge (c, d, f, e) -> (a, b, c, d, e, f, g, h)
"""
dim = 3
n_tensor = numpy.random.random((dim, dim, dim, dim))
m_tensor = numpy.random.random((dim, dim, dim, dim))
true_tensor = numpy.zeros(tuple([dim] * 8))
for a, b, c, d, e, f, g, h in product(range(dim), repeat=8):
for u_perm, u_phase in generate_parity_permutations([a, b, c, d]):
for l_perm, l_phase in generate_parity_permutations([h, g, f, e]):
# D_{hgfe}^{abcd} = C [D_{hg}^{ab}D_{fe}^{cd} +
# -1 * D_{hg}^{ab}D_{ef}^{cd} + ...]
true_tensor[a, b, c, d, e, f, g, h] += u_phase * l_phase * \
n_tensor[
u_perm[0], u_perm[1],
l_perm[1], l_perm[
0]] * m_tensor[
u_perm[2], u_perm[3],
l_perm[3], l_perm[2]]
true_tensor /= (4 * 3 * 2)**2
test_tensor = wedge(n_tensor, m_tensor, (2, 2), (2, 2))
assert numpy.allclose(test_tensor, true_tensor)
def test_random_2_1_wedge_1_1():
dim = 3
n_tensor = numpy.random.random((dim, dim, dim))
m_tensor = numpy.random.random((dim, dim))
true_tensor = numpy.zeros(tuple([dim] * 5))
for a, b, c, d, e in product(range(dim), repeat=5):
for u_perm, u_phase in generate_parity_permutations([a, b, c]):
for l_perm, l_phase in generate_parity_permutations([e, d]):
true_tensor[a, b, c, d, e] += u_phase * l_phase * n_tensor[
u_perm[0], u_perm[1], l_perm[0]] * m_tensor[u_perm[2],
l_perm[1]]
true_tensor /= (2 * 3 * 2)
test_tensor = wedge(n_tensor, m_tensor, (2, 1), (1, 1))
assert numpy.allclose(test_tensor, true_tensor)
def test_upper_lower_index_size_check():
n_tensor = numpy.zeros((2, 2, 2))
m_tensor = numpy.zeros((2, 2))
with pytest.raises(IndexError):
wedge(n_tensor, m_tensor, (3, 1), (1, 1))
with pytest.raises(IndexError):
wedge(n_tensor, m_tensor, (4, 0), (1, 2))
with pytest.raises(IndexError):
wedge(n_tensor, m_tensor, (2, 1), (1, 2))
def test_eye_wedge():
"""
Test wedge product code through identity wedge
(p, s)(q, r) - (q, s)(p, r) - (p, r)(q, s) + (q, r)(p, s)
"""
n_tensor = numpy.eye(2)
m_tensor = numpy.eye(2)
true_eye2 = numpy.zeros((2, 2, 2, 2))
for p, q, r, s in product(range(2), repeat=4):
true_eye2[p, q, r, s] += (n_tensor[p, s] * m_tensor[q, r] -
n_tensor[q, s] * m_tensor[p, r] -
n_tensor[p, r] * m_tensor[q, s] +
n_tensor[q, r] * m_tensor[p, s])
true_eye2 /= 2**2
test_eye2 = wedge(n_tensor, m_tensor, (1, 1), (1, 1))
assert numpy.allclose(test_eye2, true_eye2)
def test_random_wedge():
"""
Test wedge product code through identity wedge
(p, s)(q, r) - (q, s)(p, r) - (p, r)(q, s) + (q, r)(p, s)
"""
dim = 4
n_tensor = numpy.random.random((dim, dim))
m_tensor = numpy.random.random((dim, dim))
true_eye2 = numpy.zeros(tuple([dim] * 4))
for p, q, r, s in product(range(dim), repeat=4):
true_eye2[p, q, r, s] += (n_tensor[p, s] * m_tensor[q, r] -
n_tensor[q, s] * m_tensor[p, r] -
n_tensor[p, r] * m_tensor[q, s] +
n_tensor[q, r] * m_tensor[p, s])
true_eye2 /= 2**2
test_eye2 = wedge(n_tensor, m_tensor, (1, 1), (1, 1))
assert numpy.allclose(test_eye2, true_eye2)
def test_random_two_wedge():
"""
Test wedge product code with random 4-tensor and a random 2-tensor
(a, b, c, d) wedge (e, f) -> (a, b, e, f, c, d)
"""
dim = 3
n_tensor = numpy.random.random((dim, dim, dim, dim))
m_tensor = numpy.random.random((dim, dim))
true_tensor = numpy.zeros(tuple([dim] * 6))
for a, b, c, d, e, f in product(range(dim), repeat=6):
for u_perm, u_phase in generate_parity_permutations([a, b, c]):
for l_perm, l_phase in generate_parity_permutations([f, e, d]):
true_tensor[a, b, c, d, e, f] += u_phase * l_phase * n_tensor[
u_perm[0], u_perm[1], l_perm[1],
l_perm[0]] * m_tensor[u_perm[2], l_perm[2]]
true_tensor /= 6**2
test_tensor = wedge(n_tensor, m_tensor, (2, 2), (1, 1))
assert numpy.allclose(test_tensor, true_tensor)