More robust `isdisjoint` witness for `Interval` #3907

Original file line number	Diff line number	Diff line change
Expand Up		@@ -24,11 +24,14 @@ function _isdisjoint(I1::Interval, I2::Interval, ::Val{false})
		end

		function _isdisjoint(I1::Interval, I2::Interval, ::Val{true})
	check = _isdisjoint(I1, I2, Val(false))
	if check
	if _isdisjoint(I1, I2, Val(false))
		N = promote_type(eltype(I1), eltype(I2))
		return (true, N[])
		else
	return (false, [max(min(I1), min(I2))])
	# mid-point, most robust witness
	l = max(min(I1), min(I2))
	h = min(max(I1), max(I2))
	w = [l + (h - l) / 2]
	return (false, w)
		end
		end

20 changes: 12 additions & 8 deletions test/Sets/Interval.jl

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Original file line number	Diff line number	Diff line change
Expand Up		@@ -492,25 +492,29 @@ for N in [Float64, Float32, Rational{Int}]
		@test_throws AssertionError isdisjoint(X, X2)
		# disjoint
		Y = Interval(N(3), N(4))
	@test isdisjoint(X, Y) && isdisjoint(Y, X)
	for (pair, Z) in ((isdisjoint(X, Y, true), Y), (isdisjoint(Y, X, true), Y))
	res, w = pair
	for (Z, W) in ((X, Y), (Y, X))
	@test isdisjoint(Z, W)
	res, w = isdisjoint(Z, W, true)
		@test res && w isa Vector{N} && isempty(w)
		end
		# overlapping
		Y = Interval(N(1), N(3))
	@test !isdisjoint(X, X) && !isdisjoint(X, Y) && !isdisjoint(Y, X)
	for (pair, Z) in ((isdisjoint(X, X, true), X), (isdisjoint(X, Y, true), Y),
	(isdisjoint(Y, X, true), Y))
	res, w = pair
	@test !res && w isa Vector{N} && w ∈ X && w ∈ Z
	for (Z, W) in ((X, X), (X, Y), (Y, X))
	@test !isdisjoint(Z, W)
	res, w = isdisjoint(Z, W, true)
	@test !res && w isa Vector{N} && w ∈ Z && w ∈ W
		end
		# tolerance
		if N == Float64
		Y = Interval(2.0 + 1e-9, 3.0)
		@test !isdisjoint(X, Y)
	res, w = isdisjoint(X, Y, true)
	# TODO ∈ and isdisjoint should be consistent
	@test_broken !res && w isa Vector{N} && w ∈ X && w ∈ Y
		LazySets.set_rtol(Float64, 1e-10)
		@test isdisjoint(X, Y)
	res, w = isdisjoint(X, Y, true)
	@test res && w isa Vector{N} && isempty(w)
		# restore tolerance
		LazySets.set_rtol(Float64, LazySets.default_tolerance(Float64).rtol)
		end
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