Hessian is wrong with intervals

[dpsanders]

julia> using IntervalArithmetic, ForwardDiff, StaticArrays

julia> f(X) = ( (x, y) = X; x^2 + y^2 )
f (generic function with 2 methods)

julia> ForwardDiff.hessian(f, SVector(0..0, 0..0))
2×2 SArray{Tuple{2,2},Interval{Float64},2,4} with indices SOneTo(2)×SOneTo(2):
 [0, 2]  [0, 0]
 [0, 0]  [0, 2]

(Note that these are intervals being printed, not arrays.)
The diagonal entries are incorrect: they should be 2..2.

Cf. the same problem in
JuliaDiff/SparseDiffTools.jl#67

[KristofferC]

Is this claiming to be a bug in ForwardDiff? As the code is posted right now, ForwardDiff is not imported, and no function from ForwardDiff is being directly called.

[ChrisRackauckas]

ForwardDiff does the same exact thing with its way of seeding the Jacobian, i.e. ForwardDiff.jacobian gives the same result. Why ForwardDiff's Dual numbers do this is something we weren't able to determine. Note that directly calculating Hessian-vector products against basis vectors gives the correct result, so it's quite puzzling.

[KristofferC]

I just want a bug report towards a package to be written using the package API (or at leat some some attempt at doing so). As the issue is written right now a maintainer would be very tempted to close and say to report this to SparseDiffTools.

ForwardDiff.jacobian gives the same result.

Would be good to see the code for this then.

[dpsanders]

Sorry about that. The code is now correct.

[KristofferC]

Can't repro:

julia> using IntervalArithmetic, ForwardDiff, StaticArrays

julia> f(X) = ( (x, y) = X; x^2 + y^2 )
f (generic function with 1 method)

julia> ForwardDiff.hessian(f, SVector(0..0, 0..0))
2×2 SArray{Tuple{2,2},Interval{Float64},2,4} with indices SOneTo(2)×SOneTo(2):
 [2, 2]  [0, 0]
 [0, 0]  [2, 2]

(v1.3) pkg> st ForwardDiff
    Status `~/.julia/environments/v1.3/Project.toml`
  [f6369f11] ForwardDiff v0.10.3
  [90137ffa] StaticArrays v0.11.0

Please also post julia versions + package versions for bug reports.

[dpsanders]

Thanks that's very useful. Apparently it works correctly with the released version of IntervalArithmetic, but not the branch that I was using, so the problem seems to be there instead.

Sorry for the noise.