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Improve mince and add method for non-uniform partition of IntervalBox #467

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merged 6 commits into from
Jun 3, 2021
Merged

Improve mince and add method for non-uniform partition of IntervalBox #467

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5383884
Use broadcasting in mince
lbenet May 29, 2021
eb1d032
Add mince for non-uniform partition of IntervalBox
lbenet May 29, 2021
fae060b
Add tests
lbenet May 29, 2021
844dae4
Use dot
lbenet May 31, 2021
328b8eb
Another fix
lbenet May 31, 2021
430ed81
Avoid generating functions in mince (IntervalBox)
lbenet Jun 2, 2021
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2 changes: 1 addition & 1 deletion src/intervals/arithmetic.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -577,5 +577,5 @@ as a vector.
"""
function mince(x::Interval, n)
nodes = range(x.lo, x.hi, length = n+1)
return [Interval(nodes[i], nodes[i+1]) for i in 1:length(nodes)-1]
return @. Interval(nodes[1:n], nodes[2:n+1])
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end
20 changes: 20 additions & 0 deletions src/multidim/intervalbox.jl
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Expand Up @@ -138,6 +138,26 @@ as a vector.
end
end

@generated function mince(x::IntervalBox{N,T}, tup::NTuple{N,Int}) where {N,T}
quote
n = maximum(tup)
nodes_matrix = Array{Interval{T},2}(undef, n, N)
fill!(nodes_matrix, emptyinterval(T))
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for i in 1:N
nodes_matrix[1:tup[i],i] .= mince(x[i], tup[i])
end

nodes = IntervalBox{$N,T}[]
Base.Cartesian.@nloops $N i _->(1:n) begin
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Does this part requires carefull review? I am not familiar with the macros used, but I could delve into it if needed.

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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.

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@Kolaru Kolaru Jun 1, 2021 •
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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

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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.)

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

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I just pushed it, so you can have a look

Base.Cartesian.@nextract $N ival d->nodes_matrix[i_d, d]
ibox = Base.Cartesian.@ncall $N IntervalBox ival
isempty(ibox) || push!(nodes, ibox)
end
nodes
end
end


hull(a::IntervalBox{N,T}, b::IntervalBox{N,T}) where {N,T} = IntervalBox(hull.(a[:], b[:]))
hull(a::Vector{IntervalBox{N,T}}) where {N,T} = hull(a...)

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10 changes: 10 additions & 0 deletions test/multidim_tests/multidim.jl
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Expand Up @@ -306,18 +306,28 @@ end
@test vb2 == vv
@test hull(vb2...) == ib2
@test hull(vb2) == ib2
@test mince(ib2, (4,4)) == vb2
@test mince(ib2, (1,4)) == [ (-1 .. 1)×(-1 .. -0.5), (-1 .. 1)×(-0.5 .. 0),
(-1 .. 1)×(0 .. 0.5), (-1 .. 1)×(0.5 .. 1)]
@test hull(mince(ib2, (1,4))) == ib2

ib3 = IntervalBox(-1..1, 3)
vb3 = mince(ib3, 4)
@test length(vb3) == 4^3
@test hull(vb3...) == ib3
@test hull(vb3) == ib3
@test mince(ib3, (4,4,4)) == vb3
@test mince(ib3, (2,1,1)) == [(-1 .. 0)×(-1 .. 1)×(-1 .. 1),
(0 .. 1)×(-1 .. 1)×(-1 .. 1)]
@test hull(mince(ib3, (2,1,1))) == ib3

ib4 = IntervalBox(-1..1, 4)
vb4 = mince(ib4, 4)
@test length(vb4) == 4^4
@test hull(vb4...) == ib4
@test hull(vb4) == ib4
@test mince(ib4,(4,4,4,4)) == vb4
@test mince(ib4,(1,1,1,1)) == [ib4]
end

@testset "Special box constructors" begin
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