Differentiation of a function with nested derivatives

[pnik073]

Is it possible to calculate ADFun and its derivatives for a function that depends on nested derivatives?

Example

Let $F:\mathbb{R^n} \to \mathbb{R^1}$, which depends on $a$ and its Jacobian $J_a(\vec{x})$:

$F(\vec{x}) = f( a(\vec{x}), J_a(\vec{x} ) ) $.

I need the derivatives of $F$.

For that I need the recording for $F$ but also the recording of $a$ before I finish ( as a nested derivative ) the recording of $F$.

Currently, I get a segvault when I try to call a nested ADFun on $a$ with respect to $\vec{x}$, during the evaluation of $F$.

[bradbell]

Is J_a the Jacobian of f or the Jacobian of F ?

If it is the Jacobian of f, then yes; see
https://cppad.readthedocs.io/latest/base2ad.cpp.html

If it is the Jacobian of F, then this is a nonlinear implicit differential equation
https://en.wikipedia.org/wiki/Ordinary_differential_equation#General_definition

[pnik073]

It is the jacobian of $a(\vec{x})$

[bradbell]

OK, then you can use the technique in the base2ad example. The idea here is that you can record the function a, and the use a base2ad version of the funciton to put its derivative in another function.