Complete conversion to/from IA.Interval

docs/src/lib/conversion.md

@@ -47,7 +47,7 @@ convert(::Type{CartesianProduct{N, Interval{N}, Interval{N}}}, ::AbstractHyperre
 convert(::Type{CartesianProductArray{N, Interval{N}}}, ::AbstractHyperrectangle{N}) where {N<:Real}
 convert(::Type{Hyperrectangle}, ::Rectification{N, AH}) where {N<:Real, AH<:AbstractHyperrectangle{N}}
 convert(::Type{Interval}, ::Rectification{N, IN}) where {N<:Real, IN<:Interval{N}}
-convert(::Type{IntervalArithmetic.Interval}, ::Interval)
+convert(::Type{IntervalArithmetic.Interval}, ::ConvexSet)
 convert(::Type{Interval}, ::IntervalArithmetic.Interval)
 convert(::Type{VPolytope}, ::ConvexHullArray{N, Singleton{N, VT}}) where {N, VT}
 convert(::Type{VPolygon}, ::ConvexSet)

src/convert.jl

@@ -855,21 +855,22 @@ function convert(X::Type{HPOLYGON},
 end
 
 """
-    convert(::Type{IntervalArithmetic.Interval}, x::Interval)
+    convert(::Type{IntervalArithmetic.Interval}, X::ConvexSet)
 
-Converts a `LazySets` interval to an `Interval` from `IntervalArithmetic`.
+Converts a convex set to an `Interval` from `IntervalArithmetic`.
 
 ### Input
 
 - `Interval` -- type used for dispatch, from `IntervalArithmetic`
-- `x`        -- interval (`LazySets.Interval`)
+- `X`        -- convex set
 
 ### Output
 
 An `IntervalArithmetic.Interval`.
 """
-function convert(::Type{IntervalArithmetic.Interval}, x::Interval)
-    return IntervalArithmetic.interval(min(x), max(x))
+function convert(::Type{IntervalArithmetic.Interval}, X::ConvexSet)
+    @assert dim(X) == 1 "cannot convert a $(dim(X))-dimensional set to an interval"
+    return convert(Interval, X).dat
 end
 
 """
@@ -934,6 +935,13 @@ function convert(::Type{Hyperrectangle}, IB::IntervalArithmetic.IntervalBox)
     return Hyperrectangle(low=low_IB, high=high_IB)
 end
 
+# method for Interval
+function convert(::Type{Hyperrectangle}, I::IntervalArithmetic.Interval)
+    low_I = [IntervalArithmetic.inf(I)]
+    high_I = [IntervalArithmetic.sup(I)]
+    return Hyperrectangle(low=low_I, high=high_I)
+end
+
 """
     convert(::Type{Hyperrectangle}, r::Rectification{N, AH})
         where {N<:Real, AH<:AbstractHyperrectangle{N}}

test/Sets/Hyperrectangle.jl

@@ -235,6 +235,11 @@ for N in [Float64, Rational{Int}, Float32]
     H = convert(Hyperrectangle, B)
     @test convert(IntervalBox, H) == B
 
+    # conversion to and from IntervalArithmetic's Interval type
+    I = IntervalArithmetic.Interval(0, 1)
+    H = convert(Hyperrectangle, I)
+    @test convert(IntervalArithmetic.Interval, H) == I
+
     # conversion from other hyperrectangular sets
     H = Hyperrectangle(N[1], N[1])
     @test convert(Hyperrectangle, BallInf(N[1], N(1))) == H

test/Sets/Interval.jl

@@ -180,10 +180,13 @@ for N in [Float64, Float32, Rational{Int}]
     A = convert(Interval, H)
     @test A isa Interval && low(A) == [N(-1/2)] && high(A) == [N(1/2)]
 
-    # conversion from a lazyset to an interval
+    # conversion from a LazySet to an interval
     M = hcat(N[2])
     B = convert(Interval, M*H)
     @test B isa Interval && low(B) == [N(-1)] && high(B) == [N(1)]
+    # conversion to an IntervalArithmetic.Interval
+    B2 = convert(IntervalArithmetic.Interval, M*H)
+    @test B2 == B.dat
 
     # set difference
     A = Interval(N(5), N(8))