import logabsdetogabsdet(F::UmfpackLU) from future

This method is required for the sparse logabsdet rrules, but was
not included in Julia prior to v1.7.

Project.toml

@@ -16,6 +16,7 @@ SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SparseInverseSubset = "dc90abb0-5640-4711-901d-7e5b23a2fada"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
+SuiteSparse = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"
 
 [compat]
 Adapt = "3.4.0"

src/rulesets/SparseArrays/sparsematrix.jl

@@ -50,6 +50,40 @@ function rrule(::typeof(findnz), v::AbstractSparseVector)
     return (I, V), findnz_pullback
 end
 
+if VERSION < v"1.7"
+    #=
+    This method for `logabsdet(F::UmfpackLU)` is required to calculate the (log)determinants
+    of sparse matrices, but was not defined prior to Julia v1.7. In order fo the rrules
+    for the determinants of sparse matrices below to work, they need to be able to 
+    compute the primals as well, so this import from the future is included. For more 
+    recent versions of Julia, this definition lives in:
+    julia/stdlib/SuiteSparse/src/umfpack.jl
+    =#
+    using SuiteSparse.UMFPACK: _signperm, UmfpackLU
+
+    for itype in (:Int32, :Int64)
+        @eval begin
+            function LinearAlgebra.logabsdet(F::UmfpackLU{T, $itype}) where {T<:Union{Float64,ComplexF64}} 
+                n = checksquare(F)
+                issuccess(F) || return log(zero(real(T))), zero(T)
+                U = F.U
+                Rs = F.Rs
+                p = F.p
+                q = F.q
+                s = _signperm(p)*_signperm(q)*one(real(T))
+                P = one(T)
+                abs_det = zero(real(T))
+                @inbounds for i in 1:n
+                    dg_ii = U[i, i] / Rs[i]
+                    P *= sign(dg_ii)
+                    abs_det += log(abs(dg_ii))
+                end
+                return abs_det, s * P
+            end
+        end
+    end
+end
+
 
 function rrule(::typeof(logabsdet), x::SparseMatrixCSC)
     F = cholesky(x)