# Zygote.jl: How to get the gradient of sparse matrix

**URL:** <https://discourse.julialang.org/t/zygote-jl-how-to-get-the-gradient-of-sparse-matrix/59067>\
**Category:** General Usage\
**Tags:** question, package, differentiation, zygote, reversediff\
**Created:** [April 12, 2021, 3:03am UTC](https://discourse.julialang.org/t/zygote-jl-how-to-get-the-gradient-of-sparse-matrix/59067 "2021-04-12T03:03:39Z")\
**Posts on this page:** 1\
**Showing post:** 12

<div class="post-metadata">

**Author:** ![mohamed82008](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mohamed82008/32/18171_2.png) [@mohamed82008](https://discourse.julialang.org/u/mohamed82008)\
**Post date:** [June 13, 2023, 5:17pm UTC](https://discourse.julialang.org/t/zygote-jl-how-to-get-the-gradient-of-sparse-matrix/59067/12 "2023-06-13T17:17:20Z")

</div>

> [@mohamed82008](#):
>
> I think the answer is yes but I will need some work to back that up with a full example.

Here is an example adapted from ChainRules.

```julia
using LazyArrays, ChainRulesCore, LinearAlgebra, Zygote

mydot(x, A, y) = dot(x, A, y)

function ChainRulesCore.rrule(::typeof(mydot), x::AbstractVector{<:Number}, A::AbstractMatrix{<:Number}, y::AbstractVector{<:Number})
    z = dot(x, A, y)
    function dot_pullback(Ω̄)
        Ay = @~ A * y
        ΔΩ = unthunk(Ω̄)
        cΔΩ = conj(ΔΩ)
        dx = @~(cΔΩ .* Ay)
        ay = adjoint(y)
        dA = @~(ΔΩ .* x .* ay)
        aA = adjoint(A)
        dy = @~(ΔΩ .* (aA * x))
        return (NoTangent(), dx, dA, dy)
    end
    dot_pullback(::ZeroTangent) = (NoTangent(), ZeroTangent(), ZeroTangent(), ZeroTangent())
    return z, dot_pullback
end

```

```julia
julia> x = rand(200); A = rand(200, 300); y = rand(300);

julia> Zygote.pullback(mydot, x, A, y)[2](1.0)[2] |> Base.summarysize
4184

julia> Base.summarysize(x) + Base.summarysize(y)
4080

```

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