# Using ForwardDiff to calculate gradients of fields in composite type?

**URL:** <https://discourse.julialang.org/t/using-forwarddiff-to-calculate-gradients-of-fields-in-composite-type/6365>\
**Category:** General Usage\
**Tags:** question, differentiation\
**Created:** [October 9, 2017, 9:40pm UTC](https://discourse.julialang.org/t/using-forwarddiff-to-calculate-gradients-of-fields-in-composite-type/6365 "2017-10-09T21:40:39Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![mewilhel](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mewilhel/32/21525_2.png) [@mewilhel](https://discourse.julialang.org/u/mewilhel)\
**Post date:** [October 9, 2017, 9:40pm UTC](https://discourse.julialang.org/t/using-forwarddiff-to-calculate-gradients-of-fields-in-composite-type/6365/1 "2017-10-09T21:40:39Z")

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Hello everybody,

**A little background:**

I’m working on a package that implements creates differentiable McCormick relaxations of functions. These relaxations are generally tighter than interval bounds and since they are convex/concave in construction they are useful in a branch-and-bound optimization framework. The base object is for these are SMC:

```julia
struct SMC{T} <: AbstractMC{T}
  cc::T # concave relaxation value
  cv::T # convex relaxation value
  Intv::Interval{T} # interval over which the relaxation is defined
end

```

A library of operations is then constructed in a typical operator overloading fashion. So if one wanted to compute the relaxations of exp(-x^2)\*sin(x) at x = 2 in the interval [1,3], you’d use the following code:

```julia
x = SMC{Float64}(2,2,Interval(1,3))
y = exp(-x^2)*sin(x)
convex = y.cv
concave = y.cc

```

I’d like to be able to get gradients of y.cc and y.cv via automatic differentiation (forward or mixed type). So ultimately, I’d like to setup functions like below and use a differentiation tool to calculate gradients.

```julia
using ForwardDiff
using IntervalArithmetic

function example(x::Vector)
   Xbox = IntervalBox(-1..1,-2..2)
   temp1 = SMC{Float64}(x[1],x[1],Xbox[1])
   temp2 = SMC{Float64}(x[1],x[1],Xbox[1])
   temp3 = exp(temp1*temp2)
   temp3.cv
end

g = x -> ForwardDiff.gradient(example, x);
x0 = [1.0,2.0]
g(x0) $ gradient

```

**Is this type of automatic differentiation feasible with ForwardDiff in concept?**

I’ve been trying to get this style working for a bit and I’ve run into a lot of conversion errors with regard to Dual Numbers. So I just want to make sure this is possible before I wade deeper into this problem.

I’m almost ready to publish this package and I’ve got a separate package which includes gradient objects in SMC and naively does forward differentiation. So I can share that shortly.

Thanks for the time and consideration.

---

<div class="post-metadata">

**Author:** ![MikeInnes](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mikeinnes/32/3656_2.png) [@MikeInnes](https://discourse.julialang.org/u/MikeInnes)\
**Post date:** [October 9, 2017, 10:04pm UTC](https://discourse.julialang.org/t/using-forwarddiff-to-calculate-gradients-of-fields-in-composite-type/6365/2 "2017-10-09T22:04:27Z")

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Yes, this is definitely possible. You just have to be careful to make your code generic enough. For example, the `SMC` constructor should be deriving its type parameter from its inputs `x[1]` etc rather than being fixed to `Float64`, otherwise it won’t be able to accept the dual number type that ForwardDiff passes in.