Fix a hessian with abs

Author: OlivierHnt

ext/IntervalArithmeticDiffRulesExt.jl

@@ -1,6 +1,7 @@
 module IntervalArithmeticDiffRulesExt
 
-using IntervalArithmetic, DiffRules
+using IntervalArithmetic
+import DiffRules
 
 function DiffRules._abs_deriv(x::Interval)
     r = sign(bareinterval(x))

ext/IntervalArithmeticForwardDiffExt.jl

@@ -135,4 +135,9 @@ function (piecewise::Piecewise)(dual::Dual{T,<:Interval}) where {T}
     return Dual{T}(primal, tuple(partial...))
 end
 
+#
+
+ForwardDiff.DiffRules._abs_deriv(x::Dual{T,<:Interval}) where {T} =
+    Dual{T}(ForwardDiff.DiffRules._abs_deriv(value(x)), zero(partials(x)))
+
 end

test/interval_tests/forwarddiff.jl

@@ -21,7 +21,8 @@ end
         g(x) = abs(x)^2
         @test     ForwardDiff.derivative(g,             interval(-1, 1))   ===  interval(convert(Interval{Float64}, -2), convert(Interval{Float64}, 2), trv)
         @test all(ForwardDiff.gradient(  v -> g(v[1]), [interval(-1, 1)]) .=== [interval(convert(Interval{Float64}, -2), convert(Interval{Float64}, 2), trv)])
-        @test all(ForwardDiff.hessian(   v -> g(v[1]), [interval(  0  )]) .=== [interval(convert(Interval{Float64}, -2), convert(Interval{Float64}, 2), trv)])
+        @test all(ForwardDiff.hessian(   v -> g(v[1]), [interval(  0  )]) .=== [interval(convert(Interval{Float64}, 0.0), trv)])
+        @test all(ForwardDiff.hessian(   v -> g(v[1]), [interval(-1, 1)]) .=== [interval(convert(Interval{Float64}, -2), convert(Interval{Float64}, 2), trv)])
     end
 
     @testset "sin" begin