Superlinear scaling of build time for ParametricHamiltonians

[pablosanjose]

It seems the scaling with system size of the build time of a ParametricHamiltonian is quite bad. While allocations are perfectly under control, build time seems to be quite superlinear with the number of sites. This leads to unacceptable overhead when combining them with O(N) methods such as KPM.

(Thanks @fernandopenaranda for the heads up!)

[pablosanjose]

Upon a quick check I cannot confirm this with latest master in Julia 1.7.

julia> h! = @hopping!((t; x) -> x*t)

julia> @btime LP.honeycomb() |> hamiltonian(hopping(1)) |> unitcell(100, 100) |> parametric(h!);
  12.787 ms (612 allocations: 13.27 MiB)

julia> @btime LP.honeycomb() |> hamiltonian(hopping(1)) |> unitcell(100, 200) |> parametric(h!);
  25.778 ms (629 allocations: 24.21 MiB)

julia> @btime LP.honeycomb() |> hamiltonian(hopping(1)) |> unitcell(100, 300) |> parametric(h!);
  39.227 ms (641 allocations: 36.18 MiB)

julia> @btime LP.honeycomb() |> hamiltonian(hopping(1)) |> unitcell(100, 400) |> parametric(h!);
  48.913 ms (646 allocations: 44.09 MiB)

Seems linear to me.

@fernandopenaranda, could you confirm this is still an issue?