Fix Enzyme integration following minimal example

[Larbino1]

Enzyme autodiff fails to work with LinearSolve.

Minimal Reproducible Example 👇

using Enzyme
using LinearSolve

function testls(A, b, u)
    oa = OperatorAssumptions(true, condition = LinearSolve.OperatorCondition.WellConditioned)
    prob = LinearProblem{true}(A, b, u0=u)
    linsolve = init(prob, oa)
    solve(linsolve)
    return nothing
end


A = [1. 2.; 3. 4.]
b = [1., 2.]
u = zero(b)
dA = deepcopy(A)
db = deepcopy(b)
du = deepcopy(u)
@time testls(A, b, u)

Enzyme.autodiff(Reverse, testls, Duplicated(A, dA), Duplicated(b, db), Duplicated(u, du))

**Error & Stacktrace ⚠️**

```julia
ERROR: Enzyme execution failed.
Enzyme: Augmented forward pass custom rule Tuple{EnzymeCore.EnzymeRules.ConfigWidth{1, true, false, (false, true)}, Const{typeof(solve!)}, Type{Const{SciMLBase.LinearSolution{Float64, 1, Vector{Float64}, Nothing, LinearSolve.DefaultLinearSolver, LinearSolve.LinearCache{Matrix{Float64}, Vector{Float64}, Vector{Float64}, SciMLBase.NullParameters, LinearSolve.DefaultLinearSolver, LinearSolve.DefaultLinearSolverInit{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Vector{Int64}}, Nothing, Nothing, Nothing, LinearAlgebra.SVD{Float64, Float64, Matrix{Float64}, Vector{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int32}}, Base.RefValue{Int32}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Base.RefValue{Int64}}, LinearAlgebra.QRPivoted{Float64, Matrix{Float64}, Vector{Float64}, Vector{Int64}}, Krylov.CraigmrSolver{Float64, Float64, Vector{Float64}}, Krylov.LsmrSolver{Float64, Float64, Vector{Float64}}}, IdentityOperator, IdentityOperator, Float64, Bool}, Nothing}}}, Duplicated{LinearSolve.LinearCache{Matrix{Float64}, Vector{Float64}, Vector{Float64}, SciMLBase.NullParameters, LinearSolve.DefaultLinearSolver, LinearSolve.DefaultLinearSolverInit{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Vector{Int64}}, Nothing, Nothing, Nothing, LinearAlgebra.SVD{Float64, Float64, Matrix{Float64}, Vector{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int32}}, Base.RefValue{Int32}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Base.RefValue{Int64}}, LinearAlgebra.QRPivoted{Float64, Matrix{Float64}, Vector{Float64}, Vector{Int64}}, Krylov.CraigmrSolver{Float64, Float64, Vector{Float64}}, Krylov.LsmrSolver{Float64, Float64, Vector{Float64}}}, IdentityOperator, IdentityOperator, Float64, Bool}}} return type mismatch, expected EnzymeCore.EnzymeRules.AugmentedReturn{SciMLBase.LinearSolution{Float64, 1, Vector{Float64}, Nothing, LinearSolve.DefaultLinearSolver, LinearSolve.LinearCache{Matrix{Float64}, Vector{Float64}, Vector{Float64}, SciMLBase.NullParameters, LinearSolve.DefaultLinearSolver, LinearSolve.DefaultLinearSolverInit{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Vector{Int64}}, Nothing, Nothing, Nothing, LinearAlgebra.SVD{Float64, Float64, Matrix{Float64}, Vector{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int32}}, Base.RefValue{Int32}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Base.RefValue{Int64}}, LinearAlgebra.QRPivoted{Float64, Matrix{Float64}, Vector{Float64}, Vector{Int64}}, Krylov.CraigmrSolver{Float64, Float64, Vector{Float64}}, Krylov.LsmrSolver{Float64, Float64, Vector{Float64}}}, IdentityOperator, IdentityOperator, Float64, Bool}, Nothing}, Nothing, Any} found EnzymeCore.EnzymeRules.AugmentedReturn{SciMLBase.LinearSolution{Float64, 1, Vector{Float64}, Nothing, LinearSolve.DefaultLinearSolver, LinearSolve.LinearCache{Matrix{Float64}, Vector{Float64}, Vector{Float64}, SciMLBase.NullParameters, LinearSolve.DefaultLinearSolver, LinearSolve.DefaultLinearSolverInit{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Vector{Int64}}, Nothing, Nothing, Nothing, LinearAlgebra.SVD{Float64, Float64, Matrix{Float64}, Vector{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int32}}, Base.RefValue{Int32}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Base.RefValue{Int64}}, LinearAlgebra.QRPivoted{Float64, Matrix{Float64}, Vector{Float64}, Vector{Int64}}, Krylov.CraigmrSolver{Float64, Float64, Vector{Float64}}, Krylov.LsmrSolver{Float64, Float64, Vector{Float64}}}, IdentityOperator, IdentityOperator, Float64, Bool}, Nothing}, SciMLBase.LinearSolution{Float64, 1, Vector{Float64}, Nothing, LinearSolve.DefaultLinearSolver, LinearSolve.LinearCache{Matrix{Float64}, Vector{Float64}, Vector{Float64}, SciMLBase.NullParameters, LinearSolve.DefaultLinearSolver, LinearSolve.DefaultLinearSolverInit{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Vector{Int64}}, Nothing, Nothing, Nothing, LinearAlgebra.SVD{Float64, Float64, Matrix{Float64}, Vector{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int32}}, Base.RefValue{Int32}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Base.RefValue{Int64}}, LinearAlgebra.QRPivoted{Float64, Matrix{Float64}, Vector{Float64}, Vector{Int64}}, Krylov.CraigmrSolver{Float64, Float64, Vector{Float64}}, Krylov.LsmrSolver{Float64, Float64, Vector{Float64}}}, IdentityOperator, IdentityOperator, Float64, Bool}, Nothing}, Tuple{Vector{Float64}, Vector{Float64}, LinearSolve.LinearCache{Matrix{Float64}, Vector{Float64}, Vector{Float64}, SciMLBase.NullParameters, LinearSolve.DefaultLinearSolver, LinearSolve.DefaultLinearSolverInit{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Vector{Int64}}, Nothing, Nothing, Nothing, LinearAlgebra.SVD{Float64, Float64, Matrix{Float64}, Vector{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int32}}, Base.RefValue{Int32}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Base.RefValue{Int64}}, LinearAlgebra.QRPivoted{Float64, Matrix{Float64}, Vector{Float64}, Vector{Int64}}, Krylov.CraigmrSolver{Float64, Float64, Vector{Float64}}, Krylov.LsmrSolver{Float64, Float64, Vector{Float64}}}, IdentityOperator, IdentityOperator, Float64, Bool}, Tuple{Matrix{Float64}}, Tuple{Vector{Float64}}}}
Stacktrace:
 [1] #solve#96
   @ ./deprecated.jl:105

Stacktrace:
  [1] throwerr(cstr::Cstring)
    @ Enzyme.Compiler ~/.julia/packages/Enzyme/jOGYG/src/compiler.jl:1317
  [2] #solve#96
    @ ./deprecated.jl:105
  [3] testls
    @ ~/Dropbox (Cambridge University)/shared_Daniel/code/RobotDynamics.jl/examples/gradients/enzyme_experiments.jl:178 [inlined]
  [4] diffejulia_testls_4370wrap
    @ ~/Dropbox (Cambridge University)/shared_Daniel/code/RobotDynamics.jl/examples/gradients/enzyme_experiments.jl:0
  [5] macro expansion
    @ Enzyme.Compiler ~/.julia/packages/Enzyme/jOGYG/src/compiler.jl:5306 [inlined]
  [6] enzyme_call(::Val{…}, ::Ptr{…}, ::Type{…}, ::Type{…}, ::Val{…}, ::Type{…}, ::Type{…}, ::Const{…}, ::Type{…}, ::Duplicated{…}, ::Duplicated{…}, ::Duplicated{…})
    @ Enzyme.Compiler ~/.julia/packages/Enzyme/jOGYG/src/compiler.jl:4984
  [7] (::Enzyme.Compiler.CombinedAdjointThunk{…})(::Const{…}, ::Duplicated{…}, ::Vararg{…})
    @ Enzyme.Compiler ~/.julia/packages/Enzyme/jOGYG/src/compiler.jl:4926
  [8] autodiff(::ReverseMode{…}, ::Const{…}, ::Type{…}, ::Duplicated{…}, ::Vararg{…})
    @ Enzyme ~/.julia/packages/Enzyme/jOGYG/src/Enzyme.jl:215
  [9] autodiff(::ReverseMode{…}, ::Const{…}, ::Duplicated{…}, ::Duplicated{…}, ::Vararg{…})
    @ Enzyme ~/.julia/packages/Enzyme/jOGYG/src/Enzyme.jl:238
 [10] autodiff(::ReverseMode{…}, ::typeof(testls), ::Duplicated{…}, ::Duplicated{…}, ::Vararg{…})
    @ Enzyme ~/.julia/packages/Enzyme/jOGYG/src/Enzyme.jl:224
 [11] top-level scope
    @ ~/Dropbox (Cambridge University)/shared_Daniel/code/RobotDynamics.jl/examples/gradients/enzyme_experiments.jl:191
Some type information was truncated. Use `show(err)` to see complete types.

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