Improve mince and add method for non-uniform partition of IntervalBox

[lbenet]

Closes #444

[codecov-commenter]

Codecov Report

Merging #467 (430ed81) into master (65ca77f) will decrease coverage by 0.30%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #467      +/-   ##
==========================================
- Coverage   91.53%   91.22%   -0.31%     
==========================================
  Files          25       25              
  Lines        1748     1812      +64     
==========================================
+ Hits         1600     1653      +53     
- Misses        148      159      +11     

Impacted Files	Coverage Δ
src/intervals/arithmetic.jl	97.20% <100.00%> (ø)
src/multidim/intervalbox.jl	88.88% <100.00%> (-0.59%)	⬇️
src/intervals/conversion.jl	55.81% <0.00%> (-13.96%)	⬇️
src/intervals/rounding.jl	61.36% <0.00%> (-5.69%)	⬇️
src/intervals/macros.jl	100.00% <0.00%> (ø)
src/intervals/special.jl	100.00% <0.00%> (ø)
src/intervals/intervals.jl	94.62% <0.00%> (+3.09%)	⬆️

---

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update 65ca77f...430ed81. Read the comment docs.

[lbenet]

Some benchmarking:

• Current master:

julia> @benchmark mince(ii, ndiv) setup=(ii=-1 .. 1, ndiv=100_000_000)
BenchmarkTools.Trial: 
  memory estimate:  152.59 MiB
  allocs estimate:  2
  --------------
  minimum time:     45.498 ms (0.00% GC)
  median time:      64.020 ms (26.33% GC)
  mean time:        58.819 ms (17.82% GC)
  maximum time:     120.155 ms (58.98% GC)
  --------------
  samples:          85
  evals/sample:     1

• This PR

julia> @benchmark mince(ii, ndiv) setup=(ii=-1 .. 1, ndiv=100_000_000)
BenchmarkTools.Trial: 
  memory estimate:  152.59 MiB
  allocs estimate:  2
  --------------
  minimum time:     41.535 ms (0.00% GC)
  median time:      53.344 ms (16.84% GC)
  mean time:        54.540 ms (19.06% GC)
  maximum time:     117.183 ms (60.92% GC)
  --------------
  samples:          92
  evals/sample:     1

[Kolaru]

Does this part requires carefull review? I am not familiar with the macros used, but I could delve into it if needed.

[lbenet]

Thanks for your review @Kolaru and also for offering getting into the details of this part of the code.

Here, I simply used the original method, and adapt it to obtain the desired behavior; maybe there are better ways, but for the time being, this is good enough. The original code was inspired from this section of the manual, which admittedly I have mostly forgotten.

[Kolaru]

That sounded like a fun multidimensional challenge so I spent some time on it and I believe the following is equivalent:

function mince(x::IntervalBox{N,T}, ncuts::NTuple{N,Int}) where {N,T}
    minced_intervals = [mince(x[i], ncuts[i]) for i in 1:N]
    minced_boxes = Vector{IntervalBox{N,T}}(undef, prod(ncuts))

    for (k, cut_indices) in enumerate(CartesianIndices(ncuts))
        minced_boxes[k] = IntervalBox([minced_intervals[i][cut_indices[i]] for i in 1:N])
    end
    return minced_boxes
end

[lbenet]

Thanks @Kolaru for the suggestion! I am also changing the other method (avoiding then the @generated). I would like to include you as coauthor of this commit; is it ok with you? (I already have the commit ready, but prefer to wait for your reply before pushing it.)

[Kolaru]

Sure let me know if it needs any input from my side.

[lbenet]

I just pushed it, so you can have a look

[Kolaru]

All look good, thanks.

[lbenet]

Thanks a lot!