out of place Jacobian decomposition mutates

[clintonTE]

Performance results are highly variable when using cached out of place methods. I've gotten segfaults, although I cannot reliably reproduce that portion of the issue. Using CuArrays seems to amplify the issue.

using Revise
using Flux, BenchmarkTools, CuArrays, CUDAnative, ForwardDiff, LinearAlgebra, Random

function mwe(N, ::Type{T}=Float32) where T<:Real
  A::Matrix{T} = rand(T, N,N)
  cuA = A |> gpu

  function f!(out, A)
    out .= A .+ A .* A .+ 1f0
  end

  krn(x) = x + x*x + 1f0
  function f!(out, A::CuMatrix{Float32})
    out .= krn.(A)
  end

  function f(A)
    return A .+ A .* A .+ 1f0
  end

  function f(A::CuMatrix{Float32})
    return krn.(A)
  end

  J = rand(T, N^2, N^2)
  @info "test cpu (inplace)"
  cache = SparseDiffTools.ForwardColorJacCache(f!,A, dx = similar(A))
  SparseDiffTools.forwarddiff_color_jacobian!(J, f!, A, cache)
  (N<5) && @info "test ∇f cpu inplace: $(J)"
  (N>5) && @btime SparseDiffTools.forwarddiff_color_jacobian!($J, $f!, $A, $cache)

  @info "test cpu (out of place)"
  cacheoos = SparseDiffTools.ForwardColorJacCache(f,A, dx = similar(A))
  J = SparseDiffTools.forwarddiff_color_jacobian(f, A, cacheoos)
  (N<5) && @info "test ∇f cpu oop: $(J)"
  (N>5) && @btime SparseDiffTools.forwarddiff_color_jacobian($f, $A, $cacheoos)

  @info "test gpu (inplace)"
  cuJ = J |> gpu
  cucache = SparseDiffTools.ForwardColorJacCache(f!,cuA, dx = similar(cuA))
  SparseDiffTools.forwarddiff_color_jacobian!(cuJ, f!, cuA, cucache)
  (N<5) && @info "test ∇f gpu inplace: $(cuJ)"
  (N>5) && @btime SparseDiffTools.forwarddiff_color_jacobian!($cuJ, $f!, $cuA, $cucache)

  @info "test gpu (outofplace)"
  cucacheoop = SparseDiffTools.ForwardColorJacCache(f,cuA, dx = similar(cuA))
  cuJ = SparseDiffTools.forwarddiff_color_jacobian(f, cuA, cucacheoop)
  (N<5) && @info "test ∇f  gpu oop: $(cuJ)"
  (N>5) && @btime SparseDiffTools.forwarddiff_color_jacobian($f, $cuA, $cucacheoop)

end

mwe(12)

Output:

[ Info: test cpu (inplace)
  46.500 μs (8 allocations: 320 bytes)
[ Info: test cpu (out of place)
  181.946 ms (80271 allocations: 853.10 MiB)
[ Info: test gpu (inplace)
  12.860 ms (10965 allocations: 402.14 KiB)
[ Info: test gpu (outofplace)
  3.110 s (3516919 allocations: 122.65 MiB)

[ChrisRackauckas]

Confirmed to not be due to scalar indexing:

using Flux, SparseDiffTools, BenchmarkTools, CuArrays, ForwardDiff, LinearAlgebra, Random
CuArrays.allowscalar(false)
N = 10
T = Float32
A = rand(T, N,N)

cuA = A |> gpu

function f!(out, A)

  out .= A .+ A .* A .+ 1f0

end

krn(x) = x + x*x + 1f0

function f!(out, A::CuMatrix{Float32})

  out .= krn.(A)

end

function f(A)

  return A .+ A .* A .+ 1f0

end

function f(A::CuMatrix{Float32})

  return krn.(A)

end

J = rand(T, N^2, N^2)

@info "test cpu (inplace)"
cache = SparseDiffTools.ForwardColorJacCache(f!,A, dx = similar(A))
SparseDiffTools.forwarddiff_color_jacobian!(J, f!, A, cache)
(N<5) && @info "test ∇f cpu inplace: $(J)"
(N>5) && @btime SparseDiffTools.forwarddiff_color_jacobian!($J, $f!, $A, $cache)

@info "test cpu (out of place)"
cacheoos = SparseDiffTools.ForwardColorJacCache(f,A, dx = similar(A))
J = SparseDiffTools.forwarddiff_color_jacobian(f, A, cacheoos)
(N<5) && @info "test ∇f cpu oop: $(J)"
(N>5) && @btime SparseDiffTools.forwarddiff_color_jacobian($f, $A, $cacheoos)

@info "test gpu (inplace)"
cuJ = J |> gpu
cucache = SparseDiffTools.ForwardColorJacCache(f!,cuA, dx = similar(cuA))
SparseDiffTools.forwarddiff_color_jacobian!(cuJ, f!, cuA, cucache)
(N<5) && @info "test ∇f gpu inplace: $(cuJ)"
(N>5) && @btime SparseDiffTools.forwarddiff_color_jacobian!($cuJ, $f!, $cuA, $cucache)

@info "test gpu (outofplace)"
cucacheoop = SparseDiffTools.ForwardColorJacCache(f,cuA, dx = similar(cuA))
cuJ = SparseDiffTools.forwarddiff_color_jacobian(f, cuA, cucacheoop)
(N<5) && @info "test ∇f  gpu oop: $(cuJ)"
(N>5) && @btime SparseDiffTools.forwarddiff_color_jacobian($f, $cuA, $cucacheoop)

The problem is likely the fact that https://github.com/JuliaDiff/SparseDiffTools.jl/blob/v1.8.0/src/differentiation/compute_jacobian_ad.jl#L123-L126 produces too many kernels. It's somewhat tied up with https://github.com/JuliaDiff/SparseDiffTools.jl/pull/106 and the upstream issue https://github.com/JuliaGPU/CuArrays.jl/issues/571

[ChrisRackauckas]

https://github.com/JuliaDiff/SparseDiffTools.jl/pull/115 makes this much faster. I'll leave this open because it's not perfect (it now mutates), but the speed boost will essentially make this issue go away for most people.