fix A/x and A*x differentiation

Author: alyst

src/dual.jl

@@ -808,7 +808,7 @@ function _map_dual_components!(fvalue!, fpartial!, y::AbstractArray{DT}, x::Abst
     # y allows res to be accessed as Array{T}
     yarr = reinterpret(reshape, T, y)
     @assert size(yarr) == (N + 1, size(y)...)
-    ystride = size(y, 1)
+    ystride = size(yarr, 1)
 
     # calculate res values
     @inbounds for (j, v) in enumerate(x)
@@ -837,18 +837,21 @@ function _map_dual_components!(fvalue!, fpartial!, y::AbstractArray{DT}, x::Abst
     return y
 end
 
+function Base.:\(m::Union{LowerTriangular{<:LinearAlgebra.BlasFloat},
+                          UpperTriangular{<:LinearAlgebra.BlasFloat}},
+                 x::StridedVector{<:Dual})
+    T = valtype(eltype(x))
+    res = copy(x)
+    ldiv!(m, reinterpret(reshape, T, res)')
+    return res
+end
+
 for MT in (StridedMatrix{<:LinearAlgebra.BlasFloat},
            LowerTriangular{<:LinearAlgebra.BlasFloat},
            UpperTriangular{<:LinearAlgebra.BlasFloat})
 
-    @eval function Base.:\(m::$MT, x::StridedVector{<:Dual})
-        T = valtype(eltype(x))
-        ldiv!(m', reinterpret(reshape, T, res))
-        return res
-    end
-
     @eval Base.:\(m::$MT, x::StridedMatrix{<:Dual}) =
-        _map_dual_components!((x, _) -> ldiv!(m, x), (x, _, _) -> ldiv!(m, x), similar(x), x)
+        _map_dual_components!((y, x) -> ldiv!(y, m, x), (y, x, _) -> ldiv!(y, m, x), similar(x), x)
 
     @eval function Base.:*(m::$MT, x::StridedVector{<:Dual})
         T = valtype(eltype(x))