Add Interlace

[dlfivefifty]

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[codecov]

Codecov Report

Merging #41 into master will decrease coverage by 1.59%.
The diff coverage is 19.35%.

@@           Coverage Diff           @@
##           master    #41     +/-   ##
=======================================
- Coverage    77.6%    76%   -1.6%     
=======================================
  Files          14     15      +1     
  Lines        1143   1167     +24     
=======================================
  Hits          887    887             
- Misses        256    280     +24

Impacted Files	Coverage Δ
src/LazyArrays.jl	100% <ø> (ø)	⬆️
src/lazybroadcasting.jl	83.54% <0%> (-1.08%)	⬇️
src/interlace.jl	0% <0%> (ø)
src/lazyconcat.jl	83.72% <85.71%> (ø)	⬆️

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[DanielVandH]

Was there any particular reason this stalled if you remember @dlfivefifty? I can see a version of this for infinite arrays here

https://github.com/JuliaApproximation/AlgebraicCurveOrthogonalPolynomials.jl/blob/5bf062d232194069b4d41a35a35b86950c3ed533/src/twoband.jl#L83-L93

but a LazyInterlace could be more broadly useful here, right?

[dlfivefifty]

The whole interlace business is just in a state of mess because I wasn't entirely sure the design.

The first question is: is there a need for Interlace? Here are two synonyms:

julia> a = [1,2,3]; b = [4,5,6]; LazyBandedMatrices.BlockVec(Hcat(a,b)')
blockvec(vcat(1×3 adjoint(::Vector{Int64}) with eltype Int64, 1×3 adjoint(::Vector{Int64}) with eltype Int64)) with indices BlockedOneTo(2:2:6):
 1
 4
 ─
 2
 5
 ─
 3
 6

julia> BlockBroadcastArray(vcat, unitblocks(a), unitblocks(b))
3-blocked 6-element BlockBroadcastArray{Int64, 1, typeof(vcat), Tuple{BlockedVector{Int64, Vector{Int64}, Tuple{BlockedOneTo{Int64, Base.OneTo{Int64}}}}, BlockedVector{Int64, Vector{Int64}, Tuple{BlockedOneTo{Int64, Base.OneTo{Int64}}}}}}:
 1
 4
 ─
 2
 5
 ─
 3
 6

The second question: how to unify the different version of concatentation in ContinuumArrays.jl? See:

1. https://github.com/JuliaApproximation/ContinuumArrays.jl/blob/master/src/bases/basisconcat.jl
2. https://github.com/JuliaApproximation/ClassicalOrthogonalPolynomials.jl/blob/main/src/interlace.jl

The types defined in the latter are more thoroughly developed but I don't remember why its in ClassicalOrthogonalPolynomials.jl. It should probably be moved to ContinuumArrays.jl and unified with the types in basisconcat.jl.

We can probably discuss this in more detail at the next meeting.