Various optimizations

[andreasnoack]

This avoids a lot of dynamic dispatch by removing abstract type in the fields by making KDInternalNode and KDTree parametric on the node types and by avoiding AbstractArray as fields. At least for now, it should be fine to require Matrix and Vector either directly of via conversion. Some timings.

Current:

julia> @btime loess($(df.Speed), $(df.Dist));
  87.375 μs (2441 allocations: 847.36 KiB)

julia> @btime predict($ft, 5:25);
  27.834 μs (811 allocations: 31.22 KiB)

New:

julia> @btime loess($(df.Speed), $(df.Dist));
  77.167 μs (1886 allocations: 813.06 KiB)

julia> @btime predict($ft, 5:25);
  1.986 μs (55 allocations: 4.06 KiB)

It might still be possible to improve the speed a bit. E.g. some of the nested loops are in the wrong order but profiling suggests that most of the time in loess is spent within qr and for predict it's spent on allocating the arrays for storing the results so there shouldn't be that much performance left on the table.

Closes #47 and #51. Supersedes #53

Update: to avoid the extra type parameters, I've changed the representation of the tree to use Union{Nothing,KDNode} (where KDNode is the new name for KDInternalNode.) The performance is the same as before.

[codecov-commenter]

Codecov Report

Patch coverage: 84.09% and project coverage change: -3.27 ⚠️

Comparison is base (f02c460) 93.17% compared to head (2569c9b) 89.90%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #68      +/-   ##
==========================================
- Coverage   93.17%   89.90%   -3.27%     
==========================================
  Files           2        2              
  Lines         205      208       +3     
==========================================
- Hits          191      187       -4     
- Misses         14       21       +7     

Impacted Files	Coverage Δ
src/Loess.jl	83.80% <76.66%> (-4.31%)	⬇️
src/kd.jl	96.11% <100.00%> (-1.97%)	⬇️

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[andreasnoack]

I've pushed some changes based on your comments.

[devmotion]

Looks good to me!

to avoid the extra type parameters, I've changed the representation of the tree to use Union{Nothing,KDNode} (where KDNode is the new name for KDInternalNode.) The performance is the same as before.

That is, you see the same performance improvements as in the initial version of the PR? Good if we can avoid deeply nested types.

[andreasnoack]

That is, you see the same performance improvements as in the initial version of the PR?

Indeed. It was relative to the previous version of this PR which is much faster than current master.