Add actual file

ext/LinearSolveEnzymeExt.jl

@@ -0,0 +1,38 @@
+module LinearSolveEnzymeExt
+
+using LinearSolve
+isdefined(Base, :get_extension) ? (import Enzyme) : (import ..Enzyme)
+
+
+using Enzyme
+
+using EnzymeCore
+
+# y=inv(A) B
+#   dA −= z y^T  
+#   dB += z, where  z = inv(A^T) dy
+function EnzymeCore.EnzymeRules.augmented_primal(config::EnzymeCore.EnzymeRules.ConfigWidth{1}, func::Const{typeof(LinearSolve.solve)}, ::Type{Duplicated{RT}}, prob::Duplicated{LP}, alg::Const; kwargs...) where {RT, LP <: LinearProblem}
+    res = func.val(prob.val, alg.val; kwargs...)
+    dres = deepcopy(res)
+    dres.u .= 0
+    cache = (copy(prob.val.A), res, dres.u)
+    return EnzymeCore.EnzymeRules.AugmentedReturn{RT, RT, typeof(cache)}(res, dres, cache)
+end
+
+function EnzymeCore.EnzymeRules.reverse(config::EnzymeCore.EnzymeRules.ConfigWidth{1}, func::Const{typeof(LinearSolve.solve)}, ::Type{Duplicated{RT}}, cache, prob::Duplicated{LP}, alg::Const; kwargs...) where {RT, LP <: LinearProblem}
+    A, y, dy = cache
+
+    dA = prob.dval.A
+    db = prob.dval.b
+
+    invprob = LinearProblem(transpose(A), dy)
+
+    z = func.val(invprob, alg; kwargs...)
+
+    dA .-= z * transpose(y)
+    db .+= z
+    dy .= 0
+    return (nothing, nothing)
+end
+
+end