implement time-splines

[behinger]

• fourier
• spline
• logspaced splines
• tent (because it seems easy to do :-D)

[behinger]

I implemented spline as a starter. => See Pluto notebooks /docs/nb_timesplines.jl and ./docs/nb_timesplines_dev.jl

What I didnt really think about, is that we commonly want to move the temporal predictors from predictor space (e.g. 10 splines) back into timespace (e.g. 100 samples). I will leave this for a major overhaul of unfold :-)

[behinger]

begin
    gd = groupby(res,[:basisname,:channel,:group,:coefname])
    a = combine(gd) do d
        return undoBasis(d,m)
    end
    a
end
function undoBasis(d,m)
    bname = unique(d.basisname) # the current coefficient basename
    @assert(length(bname)==1)
    @assert(length(unique(d.channel))==1)
    bnames = unique(Unfold.get_basis_name(m)) # all model basenames

    # find out which formula / basisfunction we have
    k = findfirst(bname .== bnames) 
    bf = designmatrix(m).formulas[k].rhs.basisfunction

    estimate= bf.kernel.(0) *d.estimate
    @show size(bf.kernel.(0))
    @show size(Unfold.times(bf))
    return DataFrame(:time=>Unfold.times(bf),:estimate=>estimate)

end

This will do the trick. Now we just have to

• [ ] integreate a coeftable(m,applyBasis=true)
• [ ] unittests for multiple channels, bases, coefnames
• [ ] document