For a linear system
$$ M \dot{u} = Au \qquad \textrm{or} \qquad \dot{u} = L u $$
The generalized eigenvalue problem is $$ A e = \lambda M e $$
We can use the time-stepper approach which essentially computes the eigenvalues of the operator
$$ E = \exp(L T) $$
If $\mu$ is an eigenvalue of $E$ then it is related to the original eigenvalue by
$$ \mu = \exp(\lambda T) $$ and $T$ has to be chosen appropriately. If I have a code $E_{\Delta} \approx E$ which solves the initial value problem, then I can couple this to ARPACK to compute the eigenvalues. I would use the standard eigenvalue solver of ARPACK on the operator $E_\Delta$.
But I would also like to use the inner product induced by $M$ in the Arnoldi process so that the eigenvectors have unit norm in the inner product of $M$. How can I achieve this with ARPACK ?