Differentiation API

Derivatives of f(x::Real)::Union{Real,AbstractArray}

Gradients of f(x::AbstractArray)::Real

Jacobians of f(x::AbstractArray)::AbstractArray

Hessians of f(x::AbstractArray)::Real

Preallocating/Configuring Work Buffers

For the sake of convenience and performance, all "extra" information used by ForwardDiff's API methods is bundled up in the ForwardDiff.AbstractConfig family of types. These types allow the user to easily feed several different parameters to ForwardDiff's API methods, such as chunk size, work buffers, and perturbation seed configurations.

ForwardDiff's basic API methods will allocate these types automatically by default, but you can drastically reduce memory usage if you preallocate them yourself.

Note that for all constructors below, the chunk size N may be explicitly provided, or omitted, in which case ForwardDiff will automatically select a chunk size for you. However, it is highly recommended to specify the chunk size manually when possible (see Configuring Chunk Size).

Note also that configurations constructed for a specific function f cannot be reused to differentiate other functions (though can be reused to differentiate f at different values). To construct a configuration which can be reused to differentiate any function, you can pass nothing as the function argument. While this is more flexible, it decreases ForwardDiff's ability to catch and prevent perturbation confusion.