def test_contract():
for i in range(5):
x = np.random.randn(3, 4, 3)
y = np.random.randn(3, 4, 3)
xt = ArrayTensor(x)
yt = ArrayTensor(y)
zt = xt.contract(0, yt, 0)
assert np.sum(
(zt.array - np.einsum('ijk,ilm->jklm', x, y))**2) < epsilon
zt = xt.contract(1, yt, 1)
assert np.sum(
(zt.array - np.einsum('jik,lim->jklm', x, y))**2) < epsilon
zt = xt.contract(0, yt, 2)
assert np.sum(
(zt.array - np.einsum('ijk,lmi->jklm', x, y))**2) < epsilon
def test_IndexFactor():
for i in range(5):
x = np.random.randn(3, 4, 5, 6)
xt = ArrayTensor(x)
y = np.random.randn(3, 4, 5, 6)
yt = ArrayTensor(y)
# Compute inner product
zt = xt.contract([0], yt, [0])
# Generate a random unitary matrix
r = np.random.randn(3, 3)
r += r.T
u = expm(1j * r)
assert np.sum(
(np.identity(3) - np.dot(u, np.conjugate(u.T)))**2) < epsilon
# Apply to factors on both x and y
factX, indX = xt.getIndexFactor(0)
factY, indY = yt.getIndexFactor(0)
factX = np.tensordot(factX, u, axes=([indX], [0]))
factY = np.tensordot(factY, np.conjugate(u.T), axes=([indY], [0]))
factX = np.transpose(factX, axes=[3, 0, 1, 2])
factY = np.transpose(factY, axes=[3, 0, 1, 2])
xt = xt.setIndexFactor(0, factX)
yt = yt.setIndexFactor(0, factY)
assert xt.shape == (3, 4, 5, 6)
assert yt.shape == (3, 4, 5, 6)
zt2 = xt.contract([0], yt, [0])
assert np.sum((zt.array - zt2.array)**2) < epsilon