Fix \ for Dual

src/overloads/arrays.jl

@@ -122,6 +122,19 @@ function LinearAlgebra.:\(
     return Ainv * B
 end
 
+function LinearAlgebra.:\(
+    A::AbstractMatrix, B::AbstractVecOrMat{T}
+) where {T<:AbstractTracer}
+    return inv(A) * B
+end
+
+function LinearAlgebra.:\(
+    A::AbstractMatrix{T1}, B::AbstractVecOrMat{T2}
+) where {T1<:AbstractTracer,T2<:AbstractTracer}
+    Ainv = LinearAlgebra.pinv(A)
+    return Ainv * B
+end
+
 ## Exponential
 function Base.exp(A::AbstractMatrix{T}) where {T<:AbstractTracer}
     LinearAlgebra.checksquare(A)
@@ -187,6 +200,27 @@ 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{<:Dual}, B::AbstractVector)
+    primals, tracers = split_dual_array(A)
+    p = primals \ B
+    t = tracers \ B
+    return Dual.(p, t)
+end
+function LinearAlgebra.:\(A::AbstractMatrix, B::AbstractVector{D}) where {D<:Dual}
+    primals, tracers = split_dual_array(B)
+    p = A \ primals
+    t = A \ tracers
+    return Dual.(p, t)
+end
+function LinearAlgebra.:\(
+    A::AbstractMatrix{D1}, B::AbstractVector{D2}
+) where {D1<:Dual,D2<: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 Dual.(p, t)
+end
 
 #==============#
 # SparseArrays #

test/test_arrays.jl

@@ -399,6 +399,9 @@ end
 
     x = rand(2)
     b = A \ x
+
+    A = rand(2, 2)
+    x = [t1; t2]
     @test all(t -> sameidx(t, s_out), b)
 end
 

test/test_constructors.jl

@@ -225,3 +225,25 @@ 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)
+        A      = rand(BigFloat, 2, 2)
+        B      = rand(BigFloat, 2)
+
+        dualized_A = Dual.(A, t_full)
+        dualized_B = Dual.(B, t_full)
+        dualized_x = dualized_A \ dualized_B
+
+        @test_nowarn dualized_x = dualized_A \ dualized_B
+        @test_nowarn A \ dualized_B
+        @test_nowarn dualized_A \ B
+        @test eltype(dualized_x) == eltype(dualized_A)
+    end
+end