Implementation of an implace Hessian of a vector-valued function?

General Usage
1

HI, i’m looking to implement an implace hessian of a vector-valued function, for example:

f(x) = [x[1],x[2],sin(x[1]),sum(x)]

The ForwardDiff Documentation gives an out of place example (slightly wrong, as size(f(x)) !=size(x) in the general case:

julia> function vector_hessian(f, x)
       n = length(x)
       out = ForwardDiff.jacobian(x -> ForwardDiff.jacobian(f, x), x)
       return reshape(out, n, n, n)
   end

the problem arrives when you use a inplace version of the same function:

function f!(res,x) 
res .= [x[1],x[2],sin(x[1]),sum(x)]
end

the problem with nested inplace jacobians is that the result of the intermediate jacobian is a dual, and its very difficult to create a cache storage.
Anybody has encountered something like that? how can i create an efficient cache for this type of function?

1 Like
2

See Nested ForwardDiff.jacobian calls with inplace function - #3 by tkoolen for one solution.

2 Likes
3

Although I didn’t use the same method, the idea is here, to pass a implace Jacobian to another implace Jacobian, the cache needs to be build dinamically, and the inner jacobian should be passed as an out of place cached function.

4

And for reference, FiniteDiff.jl has a fully cached version of Hessian computations through finite differencing:

2 Likes
5

Nice! I also need to implement this on FiniteDiff (as an user selected option)

6

But the Hessian computations in FiniteDiff.jl do no support vector-valued functions, right?