  We propose a greedy algorithm for the compression of Wannier functions into
Gaussian-polynomials orbitals. The so-obtained compressed Wannier functions can
be stored in a very compact form, and can be used to efficiently parameterize
effective tight-binding Hamiltonians for multilayer 2D materials for instance.
The compression method preserves the symmetries (if any) of the original
Wannier function. We provide algorithmic details, and illustrate the
performance of our implementation on several examples, including graphene,
hexagonal boron-nitride, single-layer FeSe, and bulk silicon in the diamond
cubic structure.
