# Consistent Koopman

Julia implementations for consistent (spectral) approximations of Koopman operators, following arXiv:2309.00732 that includes a *very* limited implementation of nonlinear Laplacian spectral analysis or NLSA and related kernel algorithms. (The full and original package — implemented in Matlab — can be found here: NLSA.)

See the examples folder and flattorus.jl for the computation of approximate Koopman eigenfunctions of the flat torus system: $$\Phi^t: \mathbf{T}^2 \to \mathbf{T}^2, \Phi^t(\theta_1, \theta_2) = (\theta_1 + \alpha_1 t, \theta_2 + \alpha_2 t) \mathrm{mod} 2\pi$$ for which eigenfunctions should resemble fourier modes and the eigenvalues should be integer linear combinations of $\alpha_1$ and $\alpha_2$.

Further functionality — kernel options and more computational batching flexibility, for when memory is more limited/large datasets — to be added.