def test_irr_repr():
"""
This test tests that
- irr_repr
- compose
- spherical_harmonics
are compatible
Y(Z(alpha) Y(beta) Z(gamma) x) = D(alpha, beta, gamma) Y(x)
with x = Z(a) Y(b) eta
"""
for order in range(7):
a, b = torch.rand(2)
alpha, beta, gamma = torch.rand(3)
ra, rb, _ = compose(alpha, beta, gamma, a, b, 0)
Yrx = spherical_harmonics(order, ra, rb)
clear_spherical_harmonics_cache()
Y = spherical_harmonics(order, a, b)
clear_spherical_harmonics_cache()
DrY = irr_repr(order, alpha, beta, gamma) @ Y
d, r = (Yrx - DrY).abs().max(), Y.abs().max()
print(d.item(), r.item())
assert d < 1e-10 * r, d / r
def test_basis_transformation_Q_J():
rand_angles = torch.rand(4, 3)
J, order_out, order_in = 1, 1, 1
Q_J = basis_transformation_Q_J(J, order_in, order_out).float()
assert all(
torch.allclose(
get_R_tensor(order_out, order_in, a, b, c) @ Q_J,
Q_J @ irr_repr(J, a, b, c)) for a, b, c in rand_angles)
def sylvester_submatrix(order_out, order_in, J, a, b, c):
''' generate Kronecker product matrix for solving the Sylvester equation in subspace J '''
R_tensor = get_R_tensor(order_out, order_in, a, b,
c) # [m_out * m_in, m_out * m_in]
R_irrep_J = irr_repr(J, a, b, c) # [m, m]
R_tensor_identity = torch.eye(R_tensor.shape[0])
R_irrep_J_identity = torch.eye(R_irrep_J.shape[0])
return kron(R_tensor, R_irrep_J_identity) - kron(
R_tensor_identity,
R_irrep_J.t()) # [(m_out * m_in) * m, (m_out * m_in) * m]
def get_R_tensor(order_out, order_in, a, b, c):
return kron(irr_repr(order_out, a, b, c), irr_repr(order_in, a, b, c))