# Adapting automatic differentiation to functions with user-defined type argument

**URL:** <https://discourse.julialang.org/t/adapting-automatic-differentiation-to-functions-with-user-defined-type-argument/10707>\
**Category:** General Usage\
**Tags:** differentiation\
**Created:** [May 4, 2018, 4:23pm UTC](https://discourse.julialang.org/t/adapting-automatic-differentiation-to-functions-with-user-defined-type-argument/10707 "2018-05-04T16:23:01Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![plapplop](https://avatars.discourse-cdn.com/v4/letter/p/bbce88/32.png) [@plapplop](https://discourse.julialang.org/u/plapplop)\
**Post date:** [May 4, 2018, 4:23pm UTC](https://discourse.julialang.org/t/adapting-automatic-differentiation-to-functions-with-user-defined-type-argument/10707/1 "2018-05-04T16:23:01Z")

</div>

I’m using my own module where models can be summarized to be functions `y = f(θ)` depending on parameters `θ`, the latter being defined as a specific type `P`. I can’t change that without rewriting the whole module, which I can’t afford at the moment. I’ve written my own Jacobian function but I now want to use automatic differentiation. The problem I’m facing is that the latter only works with functions depending on `Vector`s. I’ve tried to adapt things as in the following MWE:

```julia
using ForwardDiff

type P
    a::Float64
    b::Float64
end

## convert parameters to vector
make_vector(θ::P) = map(z -> getfield(θ, z), fieldnames(θ))

## toy model
function f(θ::P)
    x = make_vector(θ)
    return sum(x) > 0.0 ? sin.(x) : cos.(x)
end

g(x::Vector) = f(P(x...))
df(θ::P) = ForwardDiff.jacobian(g, make_vector(θ))
x = [1.0, 2.0]
θ = P(x...)
dfdθ = df(θ)

```

The problem is that doing so fails because of the way `jacobian` works in the `ForwardDiff` module, I therefore get this error:

```julia
ERROR: LoadError: MethodError: Cannot `convert` an object of type ForwardDiff.Dual{ForwardDiff.Tag{#g,Float64},Float64,2} to an object of type Float64

```

Is there a way to overcome this? By keeping the signature of my models with the `P` parameters of course. Many thanks,

---

<div class="post-metadata">

**Author:** ![kristoffer.carlsson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kristoffer.carlsson/32/22_2.png) [@kristoffer.carlsson](https://discourse.julialang.org/u/kristoffer.carlsson)\
**Post date:** [May 4, 2018, 4:43pm UTC](https://discourse.julialang.org/t/adapting-automatic-differentiation-to-functions-with-user-defined-type-argument/10707/2 "2018-05-04T16:43:43Z")

</div>

Don’t hard-code `Float64` in your struct. Parameterize on the type instead.

---

<div class="post-metadata">

**Author:** ![plapplop](https://avatars.discourse-cdn.com/v4/letter/p/bbce88/32.png) [@plapplop](https://discourse.julialang.org/u/plapplop)\
**Post date:** [May 4, 2018, 4:55pm UTC](https://discourse.julialang.org/t/adapting-automatic-differentiation-to-functions-with-user-defined-type-argument/10707/3 "2018-05-04T16:55:02Z")

</div>

This indeed solved my current problem, so I at least need to remove these constraints from my models. I’ll see if this is sufficient, I may encounter other problems if some of my parameters are, say, `Array{Float64}` instead, even if they’re not hard-coded within the struct…? Anyway, thank you very much, I’ll keep you posted if I encounter new problems in the more general case.

---

<div class="post-metadata">

**Author:** ![Tamas\_Papp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tamas_papp/32/25949_2.png) [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Post date:** [May 4, 2018, 7:26pm UTC](https://discourse.julialang.org/t/adapting-automatic-differentiation-to-functions-with-user-defined-type-argument/10707/4 "2018-05-04T19:26:13Z")

</div>

> [@plapplop](#):
>
> other problems if some of my parameters are, say, `Array{Float64}` instead

The important point is to keep your code generic so that it works with all subtypes of `<: Real` (also as element types). This can frequently be accomplished by

1. simply letting Julia figure out the type (for mapping, collections, etc),
2. if you can’t do that, using constructs like `similar` (for creating arrays), `zero`, `one`, `oftype` (just look at the manual).