Jacobian-vector product (Jvp) with ForwardDiff.jl in Julia

Jacobian-vector products (also called pushforwards) are the primitives of forward sensitivity analyses. Let's use the forward-mode Automatic Differentiation capabilities of the Julia language to implement them efficiently. Also, we benchmark their performance.

A Jvp computes the result of df/dx * v, where f is a vector-valued function with a multidimensional input. Instead of naively computing the full and dense Jacobian df/dx, we can take a clever shortcut in ForwardDiff.jl

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Timestamps:
00:00 Intro
00:19 A vector-valued function
00:55 Forward-mode Automatic Differentiation with ForwardDiff.jl
01:29 Full Jacobian using ForwardDiff.jl
02:17 More interesting: Jacobian-vector product
02:44 Conceptually implementing a Jvp
03:31 More efficient Jvp with ForwardDiff.derivative
06:23 Function for naive Jvp
07:06 Benchmark clever vs. naive approach
07:49 Discussion
08:56 Outro