auto_hesvec

[ArnoStrouwen]

using ForwardDiff
function seed_duals(x::AbstractArray{V},::Type{T},::ForwardDiff.Chunk{N} = ForwardDiff.Chunk(x,typemax(Int64))) where {V,T,N} 
    seeds = ForwardDiff.construct_seeds(ForwardDiff.Partials{N,V}) 
    duals = [ForwardDiff.Dual{T}(x[i],seeds[i]) for i in eachindex(x)] 
end 
function g(x)
    x[1]^3*x[2]^3
end
x = [2.0, 3.0]
v = [4.0, 5.0]
ForwardDiff.gradient(g,x)'*v # 2376
ForwardDiff.hessian(g,x)*v # 2916 2016

test1 =  seed_duals(Dual{Nothing}.(x,v),Nothing)
ForwardDiff.partials.(g(test1).partials)

test2 = Dual{Nothing}.(seed_duals(x,Nothing),v)
g(test2).partials[1].partials

Does these make sense?

[ChrisRackauckas]

This is the more direct way to do it:

https://github.com/SciML/GalacticOptim.jl/blob/master/src/function.jl#L128-L133

It requires these overloads:

https://github.com/SciML/DiffEqFlux.jl/blob/master/src/DiffEqFlux.jl#L57-L68

It would be good to add this all here.

[ArnoStrouwen]

There are also duplicates of some jacobian free methods in
https://github.com/SciML/DiffEqSensitivity.jl/blob/25a5290013433bdadec776fa7b5a92f46e5a1777/src/derivative_wrappers.jl#L118-L123 ?

With all this duplication and scattering of methods, perhaps a DirectionalDerivative package might be a good idea?

[ChrisRackauckas]

It should all just be here, and then those packages should just depend on SparseDiffTools.jl. DiffEqFlux.jl and DiffEqSensitivity.jl just predate SparseDiffTools.jl by some time and haven't been refactored yet.

[gdalle]

Note that DifferentiationInterface.jl offers an hvp function which does exactly that, in a backend-agnostic manner and specializing on the mode combination (it chooses different methods for forward-over-reverse than reverse-over-forward for instance)

[ChrisRackauckas]

this exists