# Differentiating a function involving the adjoint of a LinearMap (LinearMaps.jl and Zygote.jl)

**URL:** <https://discourse.julialang.org/t/differentiating-a-function-involving-the-adjoint-of-a-linearmap-linearmaps-jl-and-zygote-jl/69078>\
**Category:** General Usage\
**Tags:** differentiation, linearalgebra\
**Created:** [October 1, 2021, 10:19pm UTC](https://discourse.julialang.org/t/differentiating-a-function-involving-the-adjoint-of-a-linearmap-linearmaps-jl-and-zygote-jl/69078 "2021-10-01T22:19:51Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![tictaccat](https://avatars.discourse-cdn.com/v4/letter/t/9f8e36/32.png) [@tictaccat](https://discourse.julialang.org/u/tictaccat)\
**Post date:** [October 1, 2021, 10:19pm UTC](https://discourse.julialang.org/t/differentiating-a-function-involving-the-adjoint-of-a-linearmap-linearmaps-jl-and-zygote-jl/69078/1 "2021-10-01T22:19:51Z")

</div>

Hi! I’m trying to write differentiable code using `LinearMaps.jl`. However, I am running into an issue that I just haven’t been able to fix. Below is a minimum working example of this problem.

```julia
using Zygote
using LinearMaps

struct Xop <: LinearMap{Float64}
    a::Float64
end

XopTranspose = LinearMaps.TransposeMap{<:Any, <:Xop}

Base.:(*)(X::Xop, u::AbstractVector) = X.a * u
Base.:(*)(Xt::XopTranspose, u::AbstractVector) = Xt.lmap.a .* u
Base.size(X::Xop) = (4, 4)

X = Xop(3.4)

f(a) = sum(X * a) # simple scalar-value function involving X *
g(a) = sum(X' * a) # simple scalar-value function involving X' *

println(gradient(f, collect(1:4))) # this works
println(gradient(g, collect(1:4))) # this doesn't

```

First, I subtype the `LinearMap` class to create my own operator (which just a uniform scaling). I also define an adjoint type for the operator. I make an instance of the operator, and define a function `f` involving a matrix-vector product, and a function `g` involving matrix-transpose-vector product. The function `f` differentiates just fine, but the function `g` creates an error, as shown in the log:

```julia
(Fill(3.4, 4),)
MethodError: no method matching adjoint(::NamedTuple{(:lmap,),Tuple{NamedTuple{(:a,),Tuple{Float64}}}})
Closest candidates are:
  adjoint(::Missing) at missing.jl:100
  adjoint(::ChainRulesCore.NotImplemented) at /home/gaurav/.julia/packages/ChainRulesCore/1LqRD/src/differentials/notimplemented.jl:54
  adjoint(::IRTools.Inner.CFG) at /home/gaurav/.julia/packages/IRTools/46viC/src/passes/passes.jl:29
  ...

Stacktrace:
 [1] (::Zygote.var"#back#722")(::NamedTuple{(:lmap,),Tuple{NamedTuple{(:a,),Tuple{Float64}}}}) at /home/gaurav/.julia/packages/Zygote/ajuwN/src/lib/array.jl:392
 [2] (::Zygote.var"#2930#back#723"{Zygote.var"#back#722"})(::NamedTuple{(:lmap,),Tuple{NamedTuple{(:a,),Tuple{Float64}}}}) at /home/gaurav/.julia/packages/ZygoteRules/OjfTt/src/adjoint.jl:59
 [3] g at ./In[8]:17 [inlined]
 [4] (::typeof(∂(g)))(::Float64) at /home/gaurav/.julia/packages/Zygote/ajuwN/src/compiler/interface2.jl:0
 [5] (::Zygote.var"#50#51"{typeof(∂(g))})(::Float64) at /home/gaurav/.julia/packages/Zygote/ajuwN/src/compiler/interface.jl:41
 [6] gradient(::Function, ::Array{Int64,1}) at /home/gaurav/.julia/packages/Zygote/ajuwN/src/compiler/interface.jl:76
 [7] top-level scope at In[8]:20

```

Does anyone have any idea how I can fix this issue?

---

<div class="post-metadata">

**Author:** ![goerch](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/goerch/32/29122_2.png) [@goerch](https://discourse.julialang.org/u/goerch)\
**Post date:** [October 3, 2021, 9:49am UTC](https://discourse.julialang.org/t/differentiating-a-function-involving-the-adjoint-of-a-linearmap-linearmaps-jl-and-zygote-jl/69078/2 "2021-10-03T09:49:48Z")

</div>

The following code works for me

```julia
using ForwardDiff
using LinearMaps

struct Xop <: LinearMap{Float64}
    a::Float64
end

XopTranspose = LinearMaps.TransposeMap{<:Any, <:Xop}

Base.:(*)(X::Xop, u::AbstractVector) = X.a * u
Base.:(*)(Xt::XopTranspose, u::AbstractVector) = Xt.lmap.a .* u
Base.size(X::Xop) = (4, 4)

X = Xop(3.4)

f(a) = sum(X * a) # simple scalar-value function involving X *
g(a) = sum(X' * a) # simple scalar-value function involving X' *

println(ForwardDiff.gradient(f, collect(1:4))) # this works
println(ForwardDiff.gradient(g, collect(1:4))) # this works, too

```

Looks like a problem in Zygote.jl to me?