Is there a way to chain "derivative" instructions?

[ppravatto]

I am new to the field of automatic differentiation and I was looking into it in order to migrate some of my codes from numerical differentiation (finite difference) to more accurate procedures. I often encounter multiple expressions with nested derivatives and I was wondering if there is a way to simply encode those using autodiff. I was thinking of something like the following pseudo-code:

#include <iostream>
using namespace std;

#include <autodiff/forward.hpp>
using namespace autodiff;

using dual2nd = HigherOrderDual<2>; 

dual2nd f1(dual2nd x){
    return "some_function_of_x";
}

dual2nd f2(dual2nd x){
    return "some_function_of_x";
}

// Final function for which the first derivative is needed
dual2nd g(dual2nd x){
    return f2(x) * derivative(f1, wrt(x), at(x));
}

int main(){
    dual2nd x = 2.0;
    dual2nd u = g(x);

    double dudx = derivative(g, wrt(x), at(x));

    cout << "u = " << u << endl;
    cout << "du/dx = " << dudx << endl;
}

Is possible to do something like this or am I missing something fundamental? If this is possible can you point me to some example?

[allanleal]

I would suggest not to do this in function g:

f2(x) * derivative(f1, wrt(x), at(x));

because you are mixing 2nd order dual number (the return of f2(x)) and a 1st order dual number (the return of derivative(f1, wrt(x), at(x))). If you later decide to compute 2nd order derivatives of g, you will not have 2nd order derivative contributions coming from the branch derivative(f1, wrt(x), at(x)).

Please do your experiments to see how things work.

[jusevitch]

@ppravatto Any updates on this? I'm interested in nested derivatives / gradients as well, but it's not clear how to do this. I haven't been able to get anything to work yet.

[allanleal]

Hi @jusevitch , could you please post an example of what you are trying to achieve? Maybe in a new question if not exactly the same as the one here.

[jusevitch]

Sure, I'll post a new question. Thanks for the response!

[jusevitch]

I created #255 with an example of what I have in mind.