def test_hamiltonian_eigenvectors(dtype, numpy, trotter):
"""Testing hamiltonian eigenvectors scaling."""
H1 = XXZ(nqubits=2, delta=0.5, numpy=numpy, trotter=trotter)
V1 = np.array(H1.eigenvectors())
U1 = np.array(H1.eigenvalues())
np.testing.assert_allclose(H1.matrix, V1 @ np.diag(U1) @ V1.T)
# Check ground state
np.testing.assert_allclose(H1.ground_state(), V1[:, 0])
c1 = dtype(2.5)
H2 = c1 * H1
V2 = np.array(H2._eigenvectors)
U2 = np.array(H2._eigenvalues)
np.testing.assert_allclose(H2.matrix, V2 @ np.diag(U2) @ V2.T)
c2 = dtype(-11.1)
H3 = H1 * c2
V3 = np.array(H3.eigenvectors())
U3 = np.array(H3._eigenvalues)
np.testing.assert_allclose(H3.matrix, V3 @ np.diag(U3) @ V3.T)
c3 = dtype(0)
H4 = c3 * H1
V4 = np.array(H4._eigenvectors)
U4 = np.array(H4._eigenvalues)
np.testing.assert_allclose(H4.matrix, V4 @ np.diag(U4) @ V4.T)
def test_hamiltonian_exponentiation(numpy, trotter):
from scipy.linalg import expm
H = XXZ(nqubits=2, delta=0.5, numpy=numpy, trotter=trotter)
target_matrix = expm(-0.5j * np.array(H.matrix))
np.testing.assert_allclose(H.exp(0.5), target_matrix)
H = XXZ(nqubits=2, delta=0.5, numpy=numpy, trotter=trotter)
_ = H.eigenvectors()
np.testing.assert_allclose(H.exp(0.5), target_matrix)