Fix \ for Dual

src/overloads/arrays.jl

@@ -187,6 +187,22 @@ function LinearAlgebra.logabsdet(A::AbstractMatrix{D}) where {D<:Dual}
     t1, t2 = LinearAlgebra.logabsdet(tracers)
     return (D(p1, t1), D(p2, t2))
 end
+function LinearAlgebra.:\(A::AbstractMatrix{D}, B::AbstractVector) where {D<:Dual}
+    primals, tracers = split_dual_array(A)
+    p = primals \ B
+    t = tracers \ B
+    return D.(p, t)
+end
+function LinearAlgebra.:\(A::AbstractMatrix, B::AbstractVector{D}) where {D<:Dual}
+    return D.(A) \ B
+end
+function LinearAlgebra.:\(A::AbstractMatrix{D}, B::AbstractVector{D}) where {D<:Dual}
+    A_primals, A_tracers = split_dual_array(A)
+    B_primals, B_tracers = split_dual_array(B)
+    p = A_primals \ B_primals
+    t = A_tracers \ B_tracers
+    return D.(p, t)
+end
 
 #==============#
 # SparseArrays #

test/test_constructors.jl

@@ -225,3 +225,19 @@ end
         end
     end
 end
+
+# https://github.com/adrhill/SparseConnectivityTracer.jl/issues/235
+@testset "Left division on Dual with BigFloat" begin
+    @testset "$T" for T in union(GRADIENT_TRACERS, HESSIAN_TRACERS)
+        P = IndexSetGradientPattern{Int,BitSet}
+        T = GradientTracer{P}
+
+        p      = P(BitSet(2))
+        t_full = T(p)
+
+        dualized_A = Dual.(rand(BigFloat, 2, 2), t_full)
+        dualized_B = Dual.(rand(BigFloat, 2), t_full)
+
+        @test_nowarn dualized_A \ dualized_B
+    end
+end