Issue 53: First pass at differenced AR

[seabbs]

This PR is ready for review and closes #53

[seabbs]

Any feedback before I push on?

[SamuelBrand1]

I'm still parsing this

[seabbs]

This is ready for review.

I have added unit tests but given the blocker of #126 I think we need to wait for that for the documentation (which as noted is a serious issue).

I have also opened a new PR for the differencing (#134 which I will address after this) and made an issue for the lack of consistency for positional args (#133).

[SamuelBrand1]

This looks great; love the self-referencing approach to getting generic AR/diff AR!

I think the main AR struct needs to be parametric, thats the only change I recommend.

[seabbs]

I've updated w/ all suggestions.

Note I have used @with_kw from parameters.jl vs the base implementation as it allows for assets to be placed inside the inner constructor and so makes the implementation cleaner. I have also removed the specification of p as this doesn't work well when using defaults as it starts to conflict with the inner constructor.

all issues dealt with

[seabbs]

@SamuelBrand1 pinging for review

[SamuelBrand1]

@SamuelBrand1 pinging for review

Reviewing this now

[SamuelBrand1]

LGTM, only concern is that the method isn't robust to generating vector shaped damp or ar_init.

If this gets tested and works then I'm happy

[seabbs]

This should be updated now following the approach suggested in #134 and rebased on main. Note I had to copy docstringz templates everywhere due to submodules (a good downside we should have flagged) but I think the duplication isn't that bad as its something that gets touched rarely.

Moving on to #134 now.

all changes done

[SamuelBrand1]

I like this.