# Custom adjoint for getindex in Zygote

**URL:** https://discourse.julialang.org/t/custom-adjoint-for-getindex-in-zygote/33225
**Category:** Machine Learning
**Tags:** question, zygote
**Created:** [January 11, 2020, 1:37am UTC](https://discourse.julialang.org/t/custom-adjoint-for-getindex-in-zygote/33225 "2020-01-11T01:37:25Z")
**Posts on this page:** 1
**Page:** 1

<div class="post-metadata">

### Author: ![wgm](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/wgm/32/114_2.png) [@wgm](https://discourse.julialang.org/u/wgm)
#### Post date: [January 11, 2020, 1:37am UTC](https://discourse.julialang.org/t/custom-adjoint-for-getindex-in-zygote/33225/1 "2020-01-11T01:37:25Z")

</div>

I am new to Zygote and have a question about defining my own adjoint involving `getindex` with custom indexing.

I’ve defined a type

```julia
import Base: getindex

struct ProbTensor{N}
  elements::Array{Float64,N}
end

function getindex(e::ProbTensor, idx...)
  sum(view(e.elements, (i==0 ? Colon() : (i+3)÷2 for i in idx)...))
end

```

to represent a probability distribution over N Boolean values, I’m storing false values at position 1 and true values at position 2 and I represent these values in other parts of the code as f`alse=-1`, `true=1`.

I’ve overloaded `getindex` to convert the -1/+1 indices into the array positions 1/2 and I’ve overloaded an index of 0 to correspond to marginalizing over the true and false cases. E.g. `(p::ProbTensor{3})[0,0,0]` should sum over all elements and return 1.0.

Now, I’m trying to define an adjoint for derivatives of the output of `getindex` with respect to the stored probabilities. My first attempt at the gradient of the normalization

```julia
using Zygote: gradient, @adjoint

probs = rand(2,2); probs = probs / sum(probs)

gradient(p->p[0,0], ones(2,2))

```

fails by complaining about accessing element [0,0].

So, I tried to define my own adjoint

```julia
covers(idx1::Int, idx2::Int) = idx1 == 0 || (idx1==-1 && idx2==1) || (idx1==1 && idx2==2)
covers(idxs1, idxs2::Tuple) = all(covers.(idxs1,idxs2))
covers(idxs1, idxs2::CartesianIndex) = covers(idxs1, Tuple(idxs2))

@adjoint getindex(e::ProbTensor, idx...) =
  (getindex(p, idx...), dp -> (begin
                                              arr = zeros(eltype(dp), size(dp))
                                              for i in CartesianIndices(dp)
                                                covers(idx,i) && (arr[i] = dp[i])
                                              end
                                              arr
                                           end,))

```

(covers checks for the non-zero derivative elements)

But I still get the same error. Can someone please help set me on the correct path?