  We numerically investigate topological phases of periodic lattice systems in
tight-binding description under the influence of dissipation. The effects of
dissipation are effectively described by $\mathcal{PT}$-symmetric potentials.
In this framework we develop a general numerical gauge smoothing procedure to
calculate complex Berry phases from the biorthogonal basis of the system's
non-Hermitian Hamiltonian. Further, we apply this method to a one-dimensional
$\mathcal{PT}$-symmetric lattice system and verify our numerical results by an
analytical calculation.
