Derivative of abs(::Interval) about intervalarithmetic.jl HOT 7 CLOSED

Oh no. To solve this it looks like we need to depend on ForwardDiff, possibly through package extension.

from intervalarithmetic.jl.

For the forthcoming 0.22 release, I have added DiffRules.jl as a weak dependency (so this requires Julia v1.9) and defined _abs_deriv for decorated intervals only.

This yields

julia> using IntervalArithmetic, ForwardDiff

julia> ForwardDiff.derivative(abs, interval(0)) # at 0, derivative is 0 -> trivial interval
[0.0, 0.0]_trv

julia> ForwardDiff.derivative(abs, interval(1, 2)) # 0 not in the interval -> common interval
[1.0, 1.0]_com

julia> ForwardDiff.derivative(abs, interval(0, 2)) # 0 in the interval -> trivial interval
[0.0, 1.0]_trv

julia> ForwardDiff.derivative(abs, interval(-1, 0)) # 0 in the interval -> trivial interval
[-1.0, 0.0]_trv

julia> ForwardDiff.derivative(abs, interval(-1, 1)) # 0 in the interval -> trivial interval
[-1.0, 1.0]_trv

julia> ForwardDiff.derivative(abs, interval(-2, -1))  # 0 not in the interval -> common interval
[-1.0, -1.0]_com

@agerlach, in our last discussion you mentioned how useful it is in optimisation to set the derivative of abs to 0 at 0. Does this correctly address the issue?

Note that the trivial decoration (trv) means that the resulting interval carries no meaningful information anymore. It will propagate through subsequent operations:

interval(1) + ForwardDiff.derivative(abs, interval(-1, 1)) # also has `trv` decoration
[0.0, 2.0]_trv

The use of the trivial decoration was suggested to us by @lbenet after discussing with Nathalie Revol, who is involved in the IEEE Std 1788-2015.

EDIT: you can now try this, by using the PR #593.

from intervalarithmetic.jl.

A side question: what is the result for a BareInterval?

from intervalarithmetic.jl.

It throws an error. It appears that ForwardDiff requires a subtype of Real:

julia> ForwardDiff.derivative(abs, bareinterval(0))
ERROR: MethodError: no method matching derivative(::typeof(abs), ::BareInterval{Float64})

Closest candidates are:
  derivative(::F, ::R) where {F, R<:Real}
   @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/derivative.jl:12
  derivative(::Any, ::AbstractArray)
   @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/derivative.jl:72
  derivative(::Any, ::AbstractArray, ::Real)
   @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/derivative.jl:25
  ...

Stacktrace:
 [1] top-level scope
   @ REPL[30]:1

from intervalarithmetic.jl.

Nice 😄

from intervalarithmetic.jl.

This behavior looks correct from the sub-differential perspective and correct the issue in OP.

Can you elaborate on what you mean by "decorated intervals only". I see that the returned value is decorated, but does this add requires to the input type? Also, does this lead to type-instability?

from intervalarithmetic.jl.

It requires the input to be a decorated interval, which is now simply an Interval struct since the PR #590.
No it should not lead to type-instability because it can only accept and return an Interval.

from intervalarithmetic.jl.