Work-around for explicit DAE system?

[brunomorampc]

Imagine I have

$$\dot{x}= f(x,g(x))$$

I want the diffeqsolve to return both the state and $g(x)$ at the different time points. I know from #62 that the DAE are not yet implemented, but is there a work-around that I can implement to output $g(x)$ together with the state?

[patrick-kidger]

I don't think this is a DAE. x->f(x,g(x)) gives an ODE.

And then you can evaluate g on the outputs of diffeqsolve.

[brunomorampc]

Yes, true. I did not write the complete story to avoid making it complicated but it turned out to be misleading.

I was thinking to express this as a DAE by defining like z = g(x) as a trick such that I can get that as an output of the ODE because the problem is that I do not want to re-construct the g function outside of the diffeqsolve to avoid complications in my code because that function is farely complicated and can change from applications to applications.

So I was thinking of ways the diffsolve can return this value calculated internally without me having to re-build it externally.

[patrick-kidger]

I don't think there's a way to do this in general I'm afraid. This isn't just a limitation of Diffrax, it's part of the underlying numerical methods: the points at which we evaluate the vector field are not necessarily the same as the points at which we return outputs.