In Julia, Transpose operator

Question

I am trying to use a transpose operator over a vector in order to perform am element-wise addition. For example, I want to add a column vector a = [a1;a2;a3] to a row vector b = [b1,b2] I should get matrix M = a+b = [a1+b1, a1+b2; a2+b1, a2+b2; a3+b1, a3+b2]. In MATLAB it is equivalent (if both vectors are row vectors) M = a.'+b

I am trying to get the same in Julia but here is the problem, there is no .' operator in Julia starting from 1.0 version. There is the transpose operator which does not work in broadcasting mode. The adjoint operator is not Valid for me because I work with complex numbers.

a = Vector{ComplexF64}([1+3im,2])
b = Vector{ComplexF64}([0,0,0])
Z = zeros(ComplexF64,3,2)
G = zeros(ComplexF64,3,2)


@. Z = b + a'           # Works but takes the complex conjugate
@. Z = b + transpose(a) # DOES NOT WORK!!!! The error is " DimensionMismatch("array could not be broadcast to match destination") "
Z = b .+ transpose(a)   # Works but not efficient
@. Z = b + conj(a')

The third case Z = b .+ transpose(a) is not efficient because it makes 2 loops first one for addition b .+ transpose(a), than it runs the second loop one for the assignment of b .+ transpose(a) to Z. While the other 3 cases do it within one loop. So which is the fastest way? And why transpose doesn't within Broadcasting?

Thank you in advance

user_9957710 · Answer

You can just type:

a' .+ b

Example

julia> a = ComplexF64.([1+3im,2])
2-element Array{Complex{Float64},1}:
 1.0 + 3.0im
 2.0 + 0.0im

julia> b = ComplexF64.([10,20,30])
3-element Array{Complex{Float64},1}:
 10.0 + 0.0im
 20.0 + 0.0im
 30.0 + 0.0im

julia> a' .+ b
3×2 Array{Complex{Float64},2}:
 11.0-3.0im  12.0+0.0im
 21.0-3.0im  22.0+0.0im
 31.0-3.0im  32.0+0.0im

I understand that you are worried that there is a performance penalty here. However in Julia, opposed to Matlab, transpose does not materialize data. It just provides you different indexing of the reference to the data.

In Julia, Transpose operator

1 Answers