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Rewrite IntervalBox to contain an SVector of Intervals #152

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merged 17 commits into from
Jun 3, 2018
Merged

Rewrite IntervalBox to contain an SVector of Intervals #152

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f0bda2a
Arithmetic operations and functions on IntervalBox return IntervalBox
May 15, 2018
171a7a9
Add some tests of functions on IntervalBoxes
May 16, 2018
e0114fb
More tests...
May 16, 2018
c3c6439
Rewrite IntervalBox to contain an SVector
dpsanders May 17, 2018
f4bf99c
Modify arithmetic operations for new IntervalBox
dpsanders May 17, 2018
0e4d205
Fix display of IntervalBox
dpsanders May 17, 2018
fe31ea8
Add missing functions and fix tests
dpsanders May 17, 2018
770c7d3
Rename arithmetic_functions -> arithmetic
dpsanders May 17, 2018
aeb6a5b
Fix broadcasting
dpsanders May 17, 2018
0f8cb49
Fix tests. So far no iteration for IntervalBox
dpsanders May 17, 2018
d46339c
Add setindex
dpsanders May 18, 2018
5a62f24
Add propagate_inbounds
dpsanders May 18, 2018
d6cea6e
Add iteration for IntervalBox
dpsanders May 18, 2018
818a95e
Add tests for getindex and setindex
dpsanders May 18, 2018
93bb8e0
Typo
dpsanders May 18, 2018
88b2513
Fix broadcasting and add tests
dpsanders Jun 1, 2018
ce6bcec
Fix broadcasting, take 2
dpsanders Jun 2, 2018
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3 changes: 2 additions & 1 deletion src/IntervalArithmetic.jl
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Expand Up @@ -27,7 +27,8 @@ import Base:
isfinite, isnan,
show, showall,
isinteger, setdiff,
parse
parse,
broadcast, dot, length

export
AbstractInterval, Interval,
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4 changes: 2 additions & 2 deletions src/display.jl
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Expand Up @@ -245,10 +245,10 @@ function representation(X::IntervalBox, format=nothing)
end

if display_params.format == :full
return string("IntervalBox(", join(X, ", "), ")")
return string("IntervalBox(", join(X.v, ", "), ")")

else
return join(X, " × ")
return join(X.v, " × ")
end

end
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18 changes: 18 additions & 0 deletions src/multidim/arithmetic.jl
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@@ -0,0 +1,18 @@
# This file is part of the IntervalArithmetic.jl package; MIT licensed

+(a::IntervalBox, b::IntervalBox) = IntervalBox( a.v .+ b.v )
+(a::IntervalBox, b::Real) = IntervalBox( a.v .+ b )
+(a::Real, b::IntervalBox) = IntervalBox( a .+ b.v )

-(a::IntervalBox, b::IntervalBox) = IntervalBox( a.v .- b.v )
-(a::IntervalBox, b::Real) = IntervalBox( a.v .- b )
-(a::Real, b::IntervalBox) = IntervalBox( a .- b.v )
-(a::IntervalBox) = IntervalBox( .- a.v )

*(a::IntervalBox, b::Real) = IntervalBox( a.v .* b )
*(a::Real, b::IntervalBox) = IntervalBox( a .* b.v )

/(a::IntervalBox, b::Real) = IntervalBox( a.v ./ b )

Base.broadcast(f, X::IntervalBox) = IntervalBox(f.(X.v))
Base.broadcast(f, X::IntervalBox, Y::IntervalBox) = IntervalBox( f.(X.v, Y.v) )
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Neat!

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While I truly think that this broadcasting change is very nice, I just noticed that, in order to use a function (say exp) on an IntervalBox, you do require the dot-notation. The following uses the current commit (93bb8e0) of this PR:

julia> A = IntervalBox(1..2, 3..4)
[1, 2] × [3, 4]

julia> exp.(A) # this is implemented here
[2.71828, 7.38906] × [20.0855, 54.5982]

julia> exp(A) # throwing an error here is uncomfortable!
ERROR: MethodError: no method matching exp(::IntervalArithmetic.IntervalBox{2,Float64})
Closest candidates are:
  exp(::Float16) at math.jl:950
  exp(::Complex{Float16}) at math.jl:951
  exp(::BigFloat) at mpfr.jl:517
  ...

This is sort of uncomfortable, because you force the user to write whatever functions using the dot notation instead of the usual functions. This is actually not a problem, a priori, but then it should be explicitly written somewhere. My idea with #151 was to avoid this, i.e., use directly exp(A).

Should we allow exp(A) to simply return exp.(A), or shall we leave it as it is now?

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Julia has moved to requiring exp.(v) to make explicit that you want to apply exp element-wise, since exp of a vector does not make sense.

I don't understand the context where exp of an IntervalBox makes sense. I don't actually understand your Taylor example.

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Julia has moved to requiring exp.(v) to make explicit that you want to apply exp element-wise, since exp of a vector does not make sense.

Fair enough.

35 changes: 19 additions & 16 deletions src/multidim/intervalbox.jl
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Expand Up @@ -3,53 +3,56 @@
"""An `IntervalBox` is an `N`-dimensional rectangular box, given
by a Cartesian product of `N` `Interval`s.
"""
struct IntervalBox{N,T} <: StaticVector{N, Interval{T}}
data::NTuple{N,Interval{T}}
struct IntervalBox{N,T}
v::SVector{N,Interval{T}}
end

# StaticArrays.Size{N,T}(::Type{IntervalBox{N,T}}) = StaticArrays.Size(N) # @pure not needed, I think...
Base.@propagate_inbounds Base.getindex(a::IntervalBox, i::Int) = a.data[i]
# IntervalBox(x::Interval) = IntervalBox( SVector(x) ) # single interval treated as tuple with one element

IntervalBox(x::Interval...) = IntervalBox(SVector(x))
IntervalBox(x::Tuple{T}) where {T<:Interval} = IntervalBox(SVector(x))

IntervalBox(x::Interval) = IntervalBox( (x,) ) # single interval treated as tuple with one element

Base.getindex(X::IntervalBox, i) = X.v[i]
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This replaces what it was in line 11, before; do we need Base.@propagate_inbounds here, or not?

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Good question. To be honest I'm not sure, but it probably doesn't hurt.

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I'm not sure either... I've never understood why it was needed. Proceed as you prefer.


## arithmetic operations
# Note that standard arithmetic operations are implemented automatically by FixedSizeArrays.jl

mid(X::IntervalBox) = mid.(X)
mid(X::IntervalBox) = mid.(X.v)


## set operations

# TODO: Update to use generator
⊆(X::IntervalBox{N,T}, Y::IntervalBox{N,T}) where {N,T} =
all(X .⊆ Y)
all(X.v .⊆ Y.v)

∩(X::IntervalBox{N,T}, Y::IntervalBox{N,T}) where {N,T} =
IntervalBox(X .∩ Y)
IntervalBox(X.v .∩ Y.v)
∪(X::IntervalBox{N,T}, Y::IntervalBox{N,T}) where {N,T} =
IntervalBox(X .∪ Y)
IntervalBox(X.v .∪ Y.v)

#=
On Julia 0.6 can now write
∩{N,T}(X::IntervalBox{N,T}, Y::IntervalBox{N,T}) = IntervalBox(NTuple{N, Interval{Float64}}( (X[i] ∩ Y[i]) for i in 1:N))
=#


isempty(X::IntervalBox) = any(isempty, X)
isempty(X::IntervalBox) = any(isempty, X.v)

diam(X::IntervalBox) = maximum(diam.(X))
diam(X::IntervalBox) = maximum(diam.(X.v))

emptyinterval(X::IntervalBox{N,T}) where {N,T} = IntervalBox(emptyinterval.(X))
emptyinterval(X::IntervalBox{N,T}) where {N,T} = IntervalBox(emptyinterval.(X.v))


import Base.×
×(a::Interval...) = IntervalBox(a...)
×(a::Interval, b::IntervalBox) = IntervalBox(a, b...)
×(a::IntervalBox, b::Interval) = IntervalBox(a..., b)
×(a::IntervalBox, b::IntervalBox) = IntervalBox(a..., b...)
×(a::Interval, b::IntervalBox) = IntervalBox(a, b.v...)
×(a::IntervalBox, b::Interval) = IntervalBox(a.v..., b)
×(a::IntervalBox, b::IntervalBox) = IntervalBox(a.v..., b.v...)

IntervalBox(x::Interval, ::Type{Val{n}}) where {n} = IntervalBox(SVector(ntuple(i->x, Val{n})))

IntervalBox(x::Interval, n::Int) = IntervalBox(x, Val{n})

dot(x::IntervalBox, y::IntervalBox) = dot(x.v, y.v)
length(x::IntervalBox) = length(x.v)
1 change: 1 addition & 0 deletions src/multidim/multidim.jl
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@@ -1,2 +1,3 @@
include("intervalbox.jl")
include("setdiff.jl")
include("arithmetic.jl")
4 changes: 2 additions & 2 deletions src/multidim/setdiff.jl
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Expand Up @@ -43,7 +43,7 @@ Algorithm: Start from the total overlap (in all directions);
expand each direction in turn.
"""
function setdiff(A::IntervalBox{N,T}, B::IntervalBox{N,T}) where {N,T}
X = [labelled_setdiff(a,b) for (a, b) in zip(A, B)]
X = [labelled_setdiff(a, b) for (a, b) in zip(A.v, B.v)]
# ordered such that the first in each is the excluded interval

first = [ i[1] for i in X ]
Expand All @@ -61,7 +61,7 @@ function setdiff(A::IntervalBox{N,T}, B::IntervalBox{N,T}) where {N,T}
for which in X[dimension][2:end]
excluded[dimension] = which[1]
push!(result_list,
IntervalBox(excluded[1:dimension]..., A[dimension+1:end]...))
IntervalBox(excluded[1:dimension]..., A[dimension+1:N]...))
end
end

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24 changes: 23 additions & 1 deletion test/multidim_tests/multidim.jl
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Expand Up @@ -6,9 +6,21 @@ using Base.Test
A = IntervalBox(1..2, 3..4)
B = IntervalBox(0..2, 3..6)

@test 2*A == IntervalBox(2..4, 6..8)
@test 2*A == A*2 == IntervalBox(2..4, 6..8)
@test typeof(2*A) == IntervalBox{2, Float64}
@test A + B == IntervalBox(1..4, 6..10)
@test 2 + A == IntervalBox(3..4,5..6)
@test A + 2 == IntervalBox(3..4,5..6)
@test -A == IntervalBox((-2)..(-1), (-4)..(-3))
@test 2 - A == IntervalBox(0..1, (-2)..(-1))
@test B - 2 == IntervalBox((-2)..0, 1..4)
@test dot(A, B) == @interval(9, 28)
@test A .* B == IntervalBox(0..4, 9..24)
@test A ./ A == IntervalBox((0.5)..2, (0.75)..(4/3))
@test 1 ./ B == IntervalBox((0.5)..Inf, (1/6)..(1/3))
@test B ./ 1 == B
@test A .^ 2 == IntervalBox(1..4, 9..16)
@test B .^ 0.5 == IntervalBox(@interval(0,sqrt(2)), @interval(sqrt(3),sqrt(6)))

@test A ⊆ B
@test A ∩ B == A
Expand All @@ -32,7 +44,17 @@ using Base.Test
@test isa(Y, IntervalBox)
@test length(Y) == 1
@test Y == IntervalBox( (Interval(1., 2.),) )
@test typeof(Y) == IntervalBox{1, Float64}
end

@testset "Functions on boxes" begin
A = IntervalBox(1..2, 3..4)

@test exp.(A) == IntervalBox(exp(A[1]), exp(A[2]))
@test typeof(exp.(A)) == IntervalBox{2,Float64}
@test log.(A) == IntervalBox(log(A[1]), log(A[2]))
@test sqrt.(A) == IntervalBox(sqrt(A[1]), sqrt(A[2]))
@test inv.(A) == IntervalBox(inv(A[1]), inv(A[2]))
end

# @testset "@intervalbox tests" begin
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