Convenience methods to obtain correlations in direct space

[kbarros]

Sunny currently returns all intensities in Fourier space (momentum $\mathbf{q}$ and energy $\omega$). There should be convenience functions get Fourier transformed intensities in real-space $\mathbf{r}$ and time $t$. This might need to wait until our next big interface refactor.

[Lazersmoke]

I want to flag that this issue is the main blocking feature for the "paramagnetic fitting" workflow (i.e. fitting S(Q) at high temperatures where things are short-range correlated) which is the thing that Joe's Spinteract code and some of Sakib's codes are built around. Here's an old explainer about this.

I want to highlight that this is a true missing feature and not a missing convenience function. Specifically this line:

https://github.com/SunnySuite/SunnyContributed/blob/8c82b7b69cc98ce39bccd1d1a9a4f76939baf281/initiatives/Sam-GT/realspace/classical.jl#L70

# Sunny 0.6 code
# sc :: SampledCorrelations
real_corr = real.(ifft(sc.data,(4,5,6)))

uses a Sunny-internal feature (accessing .data of a SampledCorrelations). It has to be done like this (by manipulating sc.data instead of some returned intensities) because it needs sublattice-resolved information to do the computation. So the straightforward fix is to add

struct SublatResolvedIntensities{T, Q <: AbstractQPoints, D} <: AbstractIntensities
    # Original chemical cell with na atoms
    crystal :: Crystal
    # Wavevectors in RLU
    qpts :: Q
    # Regular grid of energies
    energies :: Vector{Float64}
    # Sublattice-resolved intensity data as continuum density
    data :: Array{T, D} # (na x na x nω × nq...)
end

and output this from intensities(...) somehow (but NOT by default, since na can be large in some cases and then you explicitly don't want to deal with a big na x na x etc thing). Then, the "direct space convenience method" is something that can be implemented by the user! (so that base sunny doesn't pick up any complexity from having to deal with maintaining/documenting that conversion. The sublattice-resolved structure factor is in fact already documented in the structure factor doc!)