Implements a simple Nutpie style adaptation (using both positions and gradients, but not changing the schedule).

[nsiccha]

WIP that partially addresses #311 and supersedes #312.

There's a demo in tmp/demo.jl, which certainly does something that finishes quicker than the current default.

There are currently no additional tests, and I'm sure a few things are currently broken due to my changes.

Gonna tag @sethaxen, @aseyboldt, @svilupp, and maybe @yebai.

[nsiccha]

Gonna ask some questions before I move on:

Currently, the way I change the used mass matrix adaptor feels a bit hacky, reproduced below:

adaptor = AdvancedHMC.StanHMCAdaptor(
    AdvancedHMC.Adaptation.NutpieVar(size(metric); var=copy(metric.M⁻¹)), 
    AdvancedHMC.StepSizeAdaptor(spl.δ, integrator)
)
h, t = AdvancedHMC.sample_init(rng, hamiltonian, initial_params)
# Using the below uses Nutpie (as in position and gradients)
initial_state = AdvancedHMC.HMCState(0, t, metric, κ, adaptor)
# Using the below uses Stan (as in only positions)
# initial_state = nothing
@time samples = AdvancedHMC.sample(
    rng,
    model,
    spl,
    n_adapts + n_samples;
    n_adapts=n_adapts, initial_state,
    progress=true, 
)

Is there currently no easier way to specify what kind of adaptation to use, ideally just via some (keyword) argument to the sample function? Gonna also tag @penelopeysm and @mhauru who might know or have opinions on how to change the public API :)

[nsiccha]

After chatting with or at @penelopeysm I've opened #475 and think that this PR should only implement what it's currently doing.

I don't know whether we even want to export the defined struct currently - maybe.
In any case, I think I'll be adding new tests, docstrings, and make sure that the current tests don't fail anymore.

The main thing where I might need help is to figure out whether the needed changes to the adapt! function break things outside of this repo - which they might very well do!