Expose interpolation methods

[felixcremer]

From #14:

From the interpolation method,

function interpolate(knotxvals::Vector, knotyvals::Vector, predictxvals::AbstractVector, m::DierckXInterp, k=3)
    spl = Dierckx.Spline1D(knotxvals, knotyvals, k=k)
    #@show spl, predictxvals
    Dierckx.evaluate(spl,predictxvals)
end

the input argument m is not used. Is it possible to support other kinds of interpolation method beside spline?

[felixcremer]

It should be possible to support other interpolation methods.
What interpolations would you like to use?

Can we relay on only one external interpolations package?
Should we expose the interpolation as a function or should we do this type based?
These are a few questions I also need to think about this.

[henry2004y]

I think, it would be better to relay only on an interpolation implementation in pure Julia. I used Dierckx because Interpolations.jl didn't have an implementation of cubic splines on irregular grids, we could check, whether this is now implemented or have a look into DataInterpolations.jl

I checked that this is available through DataInterpolations.jl. It gives slightly different results compared with Dierckx's Spline1D, probably due to some implementation details. I am not aware of this pkg before, so again learned some new stuff!

[henry2004y]

Current version of Interpolations.jl still does not support unevened mesh, and I really don't like the APIs they provide. If DataInterpolations.jl can be used also in get_edgepoint, then we can stick to this pkg only. However, this pkg currently does not support proper extrapolation options.

Based on my current understanding of EMD, cubic spline method seems to be the de facto approach. While there are several papers mentioning different stopping criteria, few mention about an alternative interpolation method.

[henry2004y]

So, if I understand EMD correctly, we have to do extrapolation for the envelopes between the edge points and the first and last extrema. In this case, DataInterpolations.jl might be improper compared with Dierckx.jl.

I think we can close this for now.