add Interpolations.jl extension

[rafaqz]

This is an idea for adding an Interpolations.jl extension.

It turns out there isn't a clean way to extend Interpolations.jl methods like interpolate or scale because really on a DimArray you would always want both and have the information for both already in one object.

So the idea here (and what i personally need the most) is to define an interpolation method that lets you interpolate from one AbstractDimArray to another in a single command.

We have most of the information we need to choose the interpolation method - users can specify e.g. Cubic or Linear if they really want to. But BSpline/Gridded we know from Regular / Irregular etc.

We may also want to provide an interpolator object that can interpolate points.

I'll probably leave this here for a while until its clearer what the best strategy is, but comments are welcome.

[rafaqz]

Closes #420

@DanDeepPhase we can implement this pretty easily now. But if you have any comments on syntax or how this should work that would help. See the new tests added here for an example.

[asinghvi17]

Any particular reason this was closed?

[rafaqz]

In favour of

#609

Which needs tests, and I forgot about. And I'm not really sure on the best syntax. Feedback appreciated.

[asinghvi17]

Did #609 get merged here? I don't see the log

[rafaqz]

It got merged to the branch yes, but the PR seems dead there's no reopen button

Maybe that's just a phone app thing idk

[asinghvi17]

I guess the PR had to be reopened for the log to refresh...

[haakon-e]

Glad to find this PR. It seems the PR as-is returns an array upon interpolation

To add on to how cool this would be, here's a hacked up version that for DimVectors (but probably easy to generalize) would return a DimVector after interpolation:

function Interpolations.linear_interpolation(A::AbstractDimVector; kw...)
    function itp(pts...)
        itp = linear_interpolation(DimensionalData.index(dims(A)), A; kw...)
        valtuple = lookup(pts, dims(A))
        intp = itp(valtuple...)
        DimVector(intp, pts)
    end	
end

example:

da = cumsum(rand(X(0:0.1:1)))
itpp = linear_interpolation(da)
da_itp = itpp(X(0:0.01:1))

# plotting
f,a,s = scatter(da_itp, markersize=4, label = "new pts")
scatter!(a, da, label = "old pts")
axislegend()
f

[rafaqz]

It's just a little tricky getting the syntax right, if you want to take over find shing the PR that would help it along