searchsortedfirst of dual returning wrong result

[oscardssmith]

This is presumably caused by ForwardDiff@1.0 and is causing test failures in SciML/DataInterpolations.jl#414

julia> searchsortedfirst([0.0, 1.0, 2.0, 3.0], 1.0)
2

julia> searchsortedfirst([0.0, 1.0, 2.0, 3.0], ForwardDiff.Dual(1.0, (1.0,)))
3

[devmotion]

This is both expected and (IMO) intended: a Dual with positive partial value is strictly greater than one with the same primal but zero partial value.

[devmotion]

The change is caused by #695 which fixed the broken isless etc definitions for Duals.

[oscardssmith]

Thanks for the quick response. I agree that DataInterpolations seems to be doing some fairly sketchy things here...

[ChrisRackauckas]

The DataInterpolations derivative implementation needs to take this into account based on the continuity argument. We can take it to that repo.

[oscardssmith]

This is both expected and (IMO) intended: a Dual with positive partial value is strictly greater than one with the same primal but zero partial value.

Is it intended that for duals with multiple partials, they are compared in lexocographical order? The 1.0 behavior seems sensible for single dual duals, but somewhat random for multi dual duals:

julia> ForwardDiff.Dual(0.0, (-1.0, 1.0)) <= 0
true

julia> ForwardDiff.Dual(0.0, (-1.0, 1.0)) >= 0
false

julia> ForwardDiff.Dual(0.0, (1.0, -1.0)) <= 0
false

julia> ForwardDiff.Dual(0.0, (1.0, -1.0)) >= 0
true

[mcabbott]

Yes to lexicographical order. A quick check is:

julia> using ForwardDiff: Dual

julia> for a in (-1,0,1), b in (-1,0,1), c in (-1,0,1)
         x = Dual(0, (a, b, c))
         less = [a,b,c] < [0,0,0]
         @assert (x<0) == less
         @assert count([x<0, x==0, x>0]) == 1
       end