How can partial transposition of the Wigner function be achieved in phase space for continuous variables in non-Gaussian states?

Question

The wigner function in phase space is an equivalent description of the quantum-mechanical density matrix $\rho$. The formula for calculating negativity from the density matrix $\rho$ is $\mathscr{N}(\rho )=\frac{ ||\rho^{\rm{T}}_A||_1-1}{2}$.

It is reasonable to believe that some manipulation of the wigner function will also give negativity, the key is how to manipulate the partial transpose in wigner?

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