logdet differentiation fails

[mohamed82008]

The following example doesn't work on latest Enzyme release and Julia 1.10.

using LinearAlgebra
import Enzyme

f(x) = logdet([exp(x[1]);;])
f(rand(1))
Enzyme.gradient(Enzyme.Forward, f, rand(1))

The part of the error that I understand is:

No forward mode derivative found for dgetrf_64_
 at context:   call void @dgetrf_64_(i8* noundef nonnull %6, i8* noundef nonnull %8, i64 %23, i8* noundef nonnull %10, i64 %27, i64 noundef %bitcast_coercion42) #40 [ "jl_roots"({} addrspace(10)* null, {} addrspace(10)* %20, {} addrspace(10)* null, {} addrspace(10)* %2, {} addrspace(10)* null, {} addrspace(10)* null) ], !dbg !78

Stacktrace:
 [1] #getrf!#1
   @ ~/.julia/juliaup/julia-1.10.0-beta2+0.aarch64.apple.darwin14/share/julia/stdlib/v1.10/LinearAlgebra/src/lapack.jl:565


Stacktrace:
  [1] throwerr(cstr::Cstring)
    @ Enzyme.Compiler ~/.julia/packages/Enzyme/VS5jo/src/compiler.jl:3066
  [2] #getrf!#1
    @ ~/.julia/juliaup/julia-1.10.0-beta2+0.aarch64.apple.darwin14/share/julia/stdlib/v1.10/LinearAlgebra/src/lapack.jl:565
  [3] getrf!
    @ ~/.julia/juliaup/julia-1.10.0-beta2+0.aarch64.apple.darwin14/share/julia/stdlib/v1.10/LinearAlgebra/src/lapack.jl:557 [inlined]
  [4] #lu!#158
    @ ~/.julia/juliaup/julia-1.10.0-beta2+0.aarch64.apple.darwin14/share/julia/stdlib/v1.10/LinearAlgebra/src/lu.jl:82 [inlined]
  [5] lu!
    @ ~/.julia/juliaup/julia-1.10.0-beta2+0.aarch64.apple.darwin14/share/julia/stdlib/v1.10/LinearAlgebra/src/lu.jl:81 [inlined]
  [6] #lu#164
    @ ~/.julia/juliaup/julia-1.10.0-beta2+0.aarch64.apple.darwin14/share/julia/stdlib/v1.10/LinearAlgebra/src/lu.jl:300 [inlined]
  [7] lu (repeats 2 times)
    @ ~/.julia/juliaup/julia-1.10.0-beta2+0.aarch64.apple.darwin14/share/julia/stdlib/v1.10/LinearAlgebra/src/lu.jl:299 [inlined]
  [8] logabsdet
    @ ~/.julia/juliaup/julia-1.10.0-beta2+0.aarch64.apple.darwin14/share/julia/stdlib/v1.10/LinearAlgebra/src/generic.jl:1676 [inlined]
  [9] logdet
    @ ~/.julia/juliaup/julia-1.10.0-beta2+0.aarch64.apple.darwin14/share/julia/stdlib/v1.10/LinearAlgebra/src/generic.jl:1701
 [10] f
    @ ./REPL[7]:1 [inlined]
 [11] f
    @ ./REPL[7]:0 [inlined]
 [12] fwddiffejulia_f_2643_inner_1wrap
    @ ./REPL[7]:0
 [13] macro expansion
    @ Enzyme.Compiler ~/.julia/packages/Enzyme/VS5jo/src/compiler.jl:9774 [inlined]
 [14] enzyme_call
    @ Enzyme.Compiler ~/.julia/packages/Enzyme/VS5jo/src/compiler.jl:9452 [inlined]
 [15] ForwardModeThunk
    @ Enzyme.Compiler ~/.julia/packages/Enzyme/VS5jo/src/compiler.jl:9418 [inlined]
 [16] autodiff(::EnzymeCore.ForwardMode{…}, f::EnzymeCore.Const{…}, ::Type{…}, args::EnzymeCore.BatchDuplicated{…})
    @ Enzyme ~/.julia/packages/Enzyme/VS5jo/src/Enzyme.jl:330
 [17] autodiff
    @ Enzyme ~/.julia/packages/Enzyme/VS5jo/src/Enzyme.jl:222 [inlined]
 [18] gradient(::EnzymeCore.ForwardMode{EnzymeCore.FFIABI}, f::Function, x::Vector{Float64}; shadow::Tuple{Vector{Float64}})
    @ Enzyme ~/.julia/packages/Enzyme/VS5jo/src/Enzyme.jl:866
 [19] gradient(::EnzymeCore.ForwardMode{EnzymeCore.FFIABI}, f::Function, x::Vector{Float64})
    @ Enzyme ~/.julia/packages/Enzyme/VS5jo/src/Enzyme.jl:862
 [20] top-level scope
    @ REPL[13]:1

[wsmoses]

Yeah we don't have a derivative rule for that, want to try adding it?

[wsmoses]

Here's a bunch of samples if you'd like to take a look to get started: FluxML/NNlib.jl#536

I'd probably recommend writing the rule at the logdet function level

[mohamed82008]

Looking at the documentation, defining Enzyme rules seems somewhat mechanical. I think it might be possible to create a macro that defines an Enzyme rule using ChainRulesCore.rrule or frule. We have a macro like this for ReverseDiff and ForwardDiff.