This branch should implement the calculation of the perturbation directly in Fourier Space.
This is obtained by exploiting the relation

$$ \left<\frac{d^2V}{dR^2}\right>(q) =\left<\Upsilon u(q) \delta f(-q)\right> $$

This means that this relation can be written as block diagonal, obtaining a N-scaling speedup in case of large supercell.
Not only, this automatically impose the translational symmetry, getting an additional N scaling advantage over the fully replica symmetries algorithm currently implemented as the fast_lanczos algorithm. This implementation should therefore produce a N^2 scaling, bringing the application of Lanczos + v4 on the same computational cost as the standard SSCHA.