  The method originally developed by Kalnajs for the numerical linear stability
analysis of round galactic disks is implemented in the regimes of non-analytic
transformations between position space and angle-action space, and of vanishing
growth rates. This allows effectively any physically plausible disk to be
studied, rather than only those having analytic transformations into
angle-action space which have formed the primary focus of attention to date.
The transformations are constructed numerically using orbit integrations in
real space, and the projections of orbit radial actions on a given potential
density basis are Fourier transformed to obtain a dispersion relation in matrix
form. To verify the implementation, the fastest $m=2$ growth rates of the
isochrone and the Kuzmin-Toomre disks are recovered, and the weaker $m=2$ modes
are computed. The evolution of those growth rates as a function of the halo
mass is also calculated, and some $m=1$ modes are derived as illustration.
