Deal with ILU

Project.toml

@@ -7,6 +7,7 @@ version = "0.1.0"
 Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
 FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+IncompleteLU = "40713840-3770-5561-ab4c-a76e7d0d7895"
 Krylov = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

src/DiffKrylov.jl

@@ -3,6 +3,7 @@ module DiffKrylov
 using Krylov
 using SparseArrays
 using LinearAlgebra
+using IncompleteLU
 include("ForwardDiff/forwarddiff.jl")
 include("EnzymeRules/enzymerules.jl")
 end

src/EnzymeRules/enzymerules.jl

@@ -155,7 +155,16 @@ for AMT in (:Matrix, :SparseMatrixCSC)
                 if verbose > 0
                     @info "($psolver, $pamt) reverse"
                 end
-                _b.dval .= Krylov.$solver(transpose(A), bx[]; M=M, N=N, verbose=verbose, options...)[1]
+                N = M
+                M = N
+                if isa(M, IncompleteLU.ILUFactorization)
+                    U = copy(M.U)
+                    L = copy(M.L)
+                    transpose!(U, M.L)
+                    transpose!(L, M.U)
+                    N = IncompleteLU.ILUFactorization(L, U)
+                end
+                _b.dval .= Krylov.$solver(adjoint(A), bx[]; M=M, N=N, verbose=verbose, options...)[1]
                 _A.dval .= -x .* _b.dval'
                 return (nothing, nothing)
             end