def METHOD_NAME(dtype):
    if not nk.jax.is_complex_dtype(dtype):
        with pytest.warns(np.ComplexWarning):
            lind = nk.operator.LocalLiouvillian(ha, j_ops, dtype=dtype)
            dtype_c = nk.jax.dtype_complex(dtype)
    else:
        lind = nk.operator.LocalLiouvillian(ha, j_ops, dtype=dtype)
        dtype_c = dtype
    assert lind.dtype == dtype_c
    assert lind.hamiltonian_nh.dtype == dtype_c
    for op in lind.jump_operators:
        assert op.dtype == dtype_c
    for _dt in dtypes_r + [np.int8, np.int16]:
        sigma = op.hilbert.numbers_to_states(np.array([0, 1, 2, 3]))
        sigma = np.array(sigma, dtype=_dt)
        sigmap, mels = op.get_conn_padded(sigma)
        assert sigmap.dtype == sigma.dtype
        assert mels.dtype == lind.dtype