# Automatic differentiation of \`cispi\`
**URL:** https://discourse.julialang.org/t/automatic-differentiation-of-cispi/66075
**Category:** Optimization (Mathematical)
**Tags:** zygote, chainrulescore
**Created:** [August 9, 2021, 2:01pm UTC](https://discourse.julialang.org/t/automatic-differentiation-of-cispi/66075 "2021-08-09T14:01:42Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@RainerHeintzmann](https://discourse.julialang.org/u/RainerHeintzmann)
#### Post date: [August 9, 2021, 2:01pm UTC](https://discourse.julialang.org/t/automatic-differentiation-of-cispi/66075/1 "2021-08-09T14:01:42Z")
I think the `rrule` for `cispi` seems to be missing. Maybe it should be included in the basic set of rules?
```julia
function loss2(data)
sum(abs.(cispi.(data)))
end
data = ones(2,2)
loss2(data)
gradient(loss2, data)
```
yields:
```julia
julia> gradient(loss2, data)
ERROR: Non-differentiable function Core.Intrinsics.copysign_float
Stacktrace:
[1] error(s::String)
@ Base .\error.jl:33
[2] macro expansion
@ ~\.julia\packages\Zygote\TaBlo\src\compiler\interface2.jl:0 [inlined]
[3] (::typeof(∂(λ)))(Δ::Float64)
@ Zygote ~\.julia\packages\Zygote\TaBlo\src\compiler\interface2.jl:43
[4] Pullback
@ .\floatfuncs.jl:5 [inlined]
[5] (::typeof(∂(copysign)))(Δ::Float64)
@ Zygote ~\.julia\packages\Zygote\TaBlo\src\compiler\interface2.jl:0
[6] Pullback
@ .\special\trig.jl:885 [inlined]
[7] (::typeof(∂(sincospi)))(Δ::Tuple{Float64, Float64})
@ Zygote ~\.julia\packages\Zygote\TaBlo\src\compiler\interface2.jl:0
[8] Pullback
@ .\complex.jl:544 [inlined]
[9] #1124
@ ~\.julia\packages\Zygote\TaBlo\src\lib\broadcast.jl:192 [inlined]
[10] #4
@ .\generator.jl:36 [inlined]
[11] iterate
@ .\generator.jl:47 [inlined]
[12] collect(itr::Base.Generator{Base.Iterators.Zip{Tuple{Matrix{Tuple{ComplexF64, typeof(∂(cispi))}}, Matrix{ComplexF64}}}, Base.var"#4#5"{Zygote.var"#1124#1130"}})
@ Base .\array.jl:678
[13] map
@ .\abstractarray.jl:2383 [inlined]
[14] (::Zygote.var"#∇broadcasted#1129"{Tuple{Matrix{Float64}}, Matrix{Tuple{ComplexF64, typeof(∂(cispi))}}, Val{2}})(ȳ::Matrix{ComplexF64})
@ Zygote ~\.julia\packages\Zygote\TaBlo\src\lib\broadcast.jl:192
[15] #4008#back
@ ~\.julia\packages\ZygoteRules\OjfTt\src\adjoint.jl:59 [inlined]
[16] #209
@ ~\.julia\packages\Zygote\TaBlo\src\lib\lib.jl:203 [inlined]
[17] #1746#back
@ ~\.julia\packages\ZygoteRules\OjfTt\src\adjoint.jl:59 [inlined]
[18] Pullback
@ .\broadcast.jl:1309 [inlined]
[19] (::typeof(∂(broadcasted)))(Δ::Matrix{ComplexF64})
@ Zygote ~\.julia\packages\Zygote\TaBlo\src\compiler\interface2.jl:0
[20] Pullback
@ .\REPL[52]:2 [inlined]
[21] (::typeof(∂(loss2)))(Δ::Float64)
@ Zygote ~\.julia\packages\Zygote\TaBlo\src\compiler\interface2.jl:0
[22] (::Zygote.var"#46#47"{typeof(∂(loss2))})(Δ::Float64)
@ Zygote ~\.julia\packages\Zygote\TaBlo\src\compiler\interface.jl:41
[23] gradient(f::Function, args::Matrix{Float64})
@ Zygote ~\.julia\packages\Zygote\TaBlo\src\compiler\interface.jl:76
[24] top-level scope
@ REPL[54]:1
```
---
### Author:  [@RainerHeintzmann](https://discourse.julialang.org/u/RainerHeintzmann)
#### Post date: [August 9, 2021, 2:11pm UTC](https://discourse.julialang.org/t/automatic-differentiation-of-cispi/66075/2 "2021-08-09T14:11:51Z")
A suggestion could be:
```julia
using ChainRulesCore
function ChainRulesCore.rrule(::typeof(cispi), dat)
Y = cispi(dat)
function cispi_pullback(outer_grad)
return (NoTangent(), outer_grad .* conj.(1im .* pi .* Y))
end
return Y, cispi_pullback
end
```
but I am not sure, if this is fully efficient wrt. broadcasting, if applied to large arrays pointwise.
---
### Author:  [@mcabbott](https://discourse.julialang.org/u/mcabbott)
#### Post date: [August 9, 2021, 10:16pm UTC](https://discourse.julialang.org/t/automatic-differentiation-of-cispi/66075/3 "2021-08-09T22:16:24Z")
Indeed there is no rule. I think in ChainRules this wants to be `@scalar_rule`, would be good to have.
It does seem to work with ForwardDiff, which Zygote presently uses for (most) real but not complex-valued broadcasting:
```julia
julia> Zygote.gradient(x -> sum((real∘cispi).(x)), [0 0.5; 1 1.5])
([-0.0 -3.141592653589793; -0.0 3.141592653589793],)
julia> ForwardDiff.gradient(x -> sum(real.(cispi.(x))), [0 0.5 1 1.5])
1×4 Matrix{Float64}:
0.0 -3.14159 0.0 3.14159
```
---
### Author:  [@RainerHeintzmann](https://discourse.julialang.org/u/RainerHeintzmann)
#### Post date: [August 11, 2021, 3:27pm UTC](https://discourse.julialang.org/t/automatic-differentiation-of-cispi/66075/4 "2021-08-11T15:27:22Z")
It could be traced back to the missing `sincospi` rule, which I added (with Felix’s help) to the `ChainRules.jl` code. See this [pull request](https://github.com/JuliaDiff/ChainRules.jl/pull/497).
---
### Author:  [@simeonschaub](https://discourse.julialang.org/u/simeonschaub)
#### Post date: [August 11, 2021, 3:43pm UTC](https://discourse.julialang.org/t/automatic-differentiation-of-cispi/66075/5 "2021-08-11T15:43:20Z")
Would also be good to open an issue about a rule for `copysign` since that also shouldn’t be failing here.