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Forward Mode Automatic Differentiation for Julia

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Using the Dual implementation in ForwardDiff can be quite useful. This documents how to do it, and adds a seeding function `seed_duals` which seeds a unique partial for every component...

Hessian of vector function can be calculated by composing two jacobians: ```Julia f(x) = x.^2 g(x) = ForwardDiff.jacobian(f,x) x = rand(3) ForwardDiff.jacobian(g,x) ``` But if I want to retrieve the...

It would be great to be able to do something like ```julia val, drv = ForwardDiff.value_derivative(f, x) ```

I know it's not really well-defined to try to print a dual number like this, but it would be better if it failed more gracefully, for example by printing the...

`eps(ForwardDiff.Dual{Nothing}(1.0,1.0)) isa ForwardDiff.Dual` is false. Is this intentional? This is causing trouble in https://github.com/TuringLang/Turing.jl/issues/700.

So it works correctly with different output dimensions

Hello, I cannot use `jacobian` with `ArbFloat` type. The following code runs when `T = Float64` ```julia using ArbFloats using ForwardDiff T = Float64 # ArbFloat M = 3 F...

This likely further decreases performance when NaN-safe mode is engaged, but I think it's more correct so it's worth the perf hit either way. NaN-safe mode is already the expected...

Is it possible to use ForwardDiff to find the numerical scalar derivative of a time dependent function defined with two arrays? For example: t=[0 1 2 3 4 5 6...

We need this for TPU work so that things like `XRTArrays` can be multiplied in.