# Gradient of \`sum(f, x)\` using Zygote, when \`f\` is real valued and \`x isa CuArray{\<:Complex}\`
**URL:** https://discourse.julialang.org/t/gradient-of-sum-f-x-using-zygote-when-f-is-real-valued-and-x-isa-cuarray-complex/33081
**Category:** GPU
**Tags:** question, differentiation, zygote
**Created:** [January 8, 2020, 1:31am UTC](https://discourse.julialang.org/t/gradient-of-sum-f-x-using-zygote-when-f-is-real-valued-and-x-isa-cuarray-complex/33081 "2020-01-08T01:31:33Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@Sleort](https://discourse.julialang.org/u/Sleort)
#### Post date: [January 8, 2020, 1:31am UTC](https://discourse.julialang.org/t/gradient-of-sum-f-x-using-zygote-when-f-is-real-valued-and-x-isa-cuarray-complex/33081/1 "2020-01-08T01:31:33Z")
While I’m able to differentiate `sum(abs2, a)` (using Zygote) when `a isa CuArray{<:Complex}`, this fails for `sum(f, a)` with `f = abs2` [see below for details]. I haven’t been able to figure out exactly why – and how to fix this. Anyone (probably @maleadt 🙂 )?
MWE:
```julia
using CuArrays
using Zygote
import GPUArrays
f(x) = abs2(x) #Test function. Eventually, I'd like to be able to use an arbitrary real valued function f...
CuArrays.@cufunc f(x) = abs2(x) #For using f with CuArrays
GPUArrays.gpu_promote_type(::typeof(f), ::Type{Complex{T}}) where {T} = T #"hack" such that sum(f, a) isa Real
a_cpu = randn(ComplexF32, 100, 100)
a_gpu = cu(a_cpu)
sum(f, a_gpu) #OKAY
gradient(x -> sum(f, x), a_cpu) #OKAY on CPU with f
gradient(x -> sum(f, x), real(a_gpu)) #OKAY on GPU with f if the input is real
gradient(x -> sum(abs2, x), a_gpu) #OKAY on GPU with abs2
gradient(x -> sum(f, x), a_gpu) #ERROR on GPU with f
```
The error message reads
```julia
ERROR: MethodError: no method matching iterate(::Nothing)
Closest candidates are:
iterate(::Core.SimpleVector) at essentials.jl:600
iterate(::Core.SimpleVector, ::Any) at essentials.jl:600
iterate(::ExponentialBackOff) at error.jl:218
...
Stacktrace:
[1] (::Zygote.var"#1728#1732"{Zygote.var"#1599#1603"})(::CuArray{Float32,2,Nothing}) at /home/troels/.julia/packages/Zygote/R2pFS/src/lib/broadcast.jl:179
[2] (::Zygote.var"#661#back#1733"{Zygote.var"#1728#1732"{Zygote.var"#1599#1603"}})(::CuArray{Float32,2,Nothing}) at /home/troels/.julia/packages/ZygoteRules/6nssF/src/adjoint.jl:49
[3] (::Zygote.var"#157#158"{Zygote.var"#661#back#1733"{Zygote.var"#1728#1732"{Zygote.var"#1599#1603"}},Tuple{Tuple{Nothing,Nothing,Nothing},Tuple{}}})(::CuArray{Float32,2,Nothing}) at /home/troels/.julia/packages/Zygote/R2pFS/src/lib/lib.jl:156
[4] (::Zygote.var"#297#back#159"{Zygote.var"#157#158"{Zygote.var"#661#back#1733"{Zygote.var"#1728#1732"{Zygote.var"#1599#1603"}},Tuple{Tuple{Nothing,Nothing,Nothing},Tuple{}}}})(::CuArray{Float32,2,Nothing}) at /home/troels/.julia/packages/ZygoteRules/6nssF/src/adjoint.jl:49
[5] #1135 at ./broadcast.jl:1231 [inlined]
[6] (::typeof(∂(#1135)))(::Float32) at /home/troels/.julia/packages/Zygote/R2pFS/src/compiler/interface2.jl:0
[7] (::Zygote.var"#28#29"{typeof(∂(#1135))})(::Float32) at /home/troels/.julia/packages/Zygote/R2pFS/src/compiler/interface.jl:38
[8] (::Zygote.var"#1136#1138"{Zygote.var"#28#29"{typeof(∂(#1135))}})(::Float32) at /home/troels/.julia/packages/Zygote/R2pFS/src/lib/array.jl:170
[9] #17 at ./none:1 [inlined]
[10] (::typeof(∂(#17)))(::Float32) at /home/troels/.julia/packages/Zygote/R2pFS/src/compiler/interface2.jl:0
[11] (::Zygote.var"#28#29"{typeof(∂(#17))})(::Float32) at /home/troels/.julia/packages/Zygote/R2pFS/src/compiler/interface.jl:38
[12] gradient(::Function, ::CuArray{Complex{Float32},2,Nothing}) at /home/troels/.julia/packages/Zygote/R2pFS/src/compiler/interface.jl:47
[13] top-level scope at none:0
```
Additional info:
```julia
(v1.3) pkg> st CuArrays
Status `~/.julia/environments/v1.3/Project.toml`
[79e6a3ab] Adapt v1.0.0
[fa961155] CEnum v0.2.0
[3895d2a7] CUDAapi v2.1.0
[c5f51814] CUDAdrv v5.0.1
[be33ccc6] CUDAnative v2.7.0
[3a865a2d] CuArrays v1.6.0 #master (https://github.com/JuliaGPU/CuArrays.jl.git)
[864edb3b] DataStructures v0.17.7
[0c68f7d7] GPUArrays v2.0.1 #master (https://github.com/JuliaGPU/GPUArrays.jl.git)
[872c559c] NNlib v0.6.2
(v1.3) pkg> st Zygote
Status `~/.julia/environments/v1.3/Project.toml`
[7a1cc6ca] FFTW v1.2.0
[f6369f11] ForwardDiff v0.10.8
[7869d1d1] IRTools v0.3.0
[872c559c] NNlib v0.6.2
[276daf66] SpecialFunctions v0.9.0
[e88e6eb3] Zygote v0.4.3 #master (https://github.com/FluxML/Zygote.jl.git)
[700de1a5] ZygoteRules v0.2.0
```
(Note: I asked the same question – without luck – on Slack #gpu yesterday, but realized that this might be a better place to do so…)
---
### Author:  [@maleadt](https://discourse.julialang.org/u/maleadt)
#### Post date: [January 8, 2020, 6:58am UTC](https://discourse.julialang.org/t/gradient-of-sum-f-x-using-zygote-when-f-is-real-valued-and-x-isa-cuarray-complex/33081/2 "2020-01-08T06:58:01Z")
Although there’s likely something wrong with CuArrays functionality here, I don’t have enough Zygote experience to know what’s up.