Update ext/LinearSolveMooncakeExt.jl

Author: ChrisRackauckas

ext/LinearSolveMooncakeExt.jl

@@ -87,7 +87,7 @@ function Mooncake.rrule!!(::CoDual{typeof(SciMLBase.solve!)}, _cache::CoDual{<:L
 
     function solve!_adjoint(::NoRData)
         ∂∅ = NoRData()
-        cachenew = init(LinearProblem(cache.A, cache.b), LUFactorization(), _args...; kwargs...)
+        cachenew = init(LinearProblem(cache.A, cache.b), cache.alg, _args...; kwargs...)
         new_sol = solve!(cachenew)
         ∂u = sol.dx.data.u