I just got bitten by some unexpected behavior of vec() in julia 0.7. When I run the code below
N = 3
A = randn(N,N) + im .* randn(N,N)
x = randn(N)
z = x'*A
vec(z)
I get this:
julia> N = 3
3
julia> A = randn(N,N) + im .* randn(N,N)
3×3 Array{Complex{Float64},2}:
0.382542-0.266179im -1.69847+1.86236im 1.28885+0.694938im
-0.177623-0.213032im -0.607246+0.719279im -2.87126+1.34141im
0.565711-0.303921im -1.38508+0.684031im 0.416797-0.26476im
julia> x = randn(N)
3-element Array{Float64,1}:
-0.00922375082321524
-0.0683463031968038
-0.29722269002054613
julia> z = x'*A
1×3 LinearAlgebra.Adjoint{Complex{Float64},Array{Complex{Float64},1}}:
-0.159531+0.107347im 0.468845-0.269648im 0.0604705-0.0193976im
julia> vec(z)
3-element Array{Complex{Float64},1}:
-0.1595307578638994 - 0.10734716516787285im
0.4688454575032254 + 0.2696475874174454im
0.060470534170491766 + 0.019397566097290375im
Notice that vec(), besides reshaping z, also computes its conjugate. Things work differently in 1.1 though:
julia> N = 3
3
julia> A = randn(N,N) + im .* randn(N,N)
3×3 Array{Complex{Float64},2}:
2.30835+1.173im 0.777158-2.76038im -0.434369+1.84468im
-0.0812661-0.674808im 1.3555+0.468595im -0.104688+0.238554im
-0.649005+0.0857933im -0.556948-0.524496im -1.19101+0.45196im
julia> x = randn(N)
3-element Array{Float64,1}:
-0.10756799853360234
-1.5958910088917135
-0.9507274395938174
julia> z = x'*A
1×3 LinearAlgebra.Adjoint{Complex{Float64},Array{Complex{Float64},1}}:
0.498415+0.869177im -1.71732+0.0477544im 1.34612-1.00883im
julia> vec(z)
3-element reshape(::LinearAlgebra.Adjoint{Complex{Float64},Array{Complex{Float64},1}}, 3) with eltype Complex{Float64}:
0.4984145172595025 + 0.8691770844949784im
-1.717324546759147 + 0.047754399003301196im
1.3461160206833889 - 1.0088254082365649im
Since the behavior of vec() changed from 0.7 to 1.1 (I didn’t test this on 1.0), I guess this has been discussed somewhere. I did a quick search but couldn’t find anything though. Does anybody know anything about this?