kron product of vector of vectors with a vector seems misordered

[rapus95]

julia> kron([[1,2],[3,4]], [4,5])
4-element Array{Array{Int64,1},1}:
 [4, 8]
 [5, 10]
 [12, 16]
 [15, 20]

as far as I can tell, the order here should be

4-element Array{Array{Int64,1},1}:
 [4, 8]
 [12, 16]
 [5, 10]
 [15, 20]

Or what's wrong with my mind?

[jebej]

There isn't yet good support for kron with arrays of arrays. However, if you asked me what the operation above should give it would be [[4,5,8,10], [12,15,16,20]].
This is equivalent to treating [[1,2],[3,4]] as a block matrix version of [1,2,3,4], and so should give the same result.

You can currently do this by passing [4,5] as a block matrix too, with a single block [[4,5]] and using a dot kron:

julia> kron.([[1,2],[3,4]], [[4,5]])
2-element Array{Array{Int64,1},1}:
 [4, 5, 8, 10]
 [12, 15, 16, 20]

Correspondingly, the non-block matrix version gives the same thing:

julia> kron([1,2,3,4], [4,5])
8-element Array{Int64,1}:    
  4                          
  5                          
  8                          
 10                          
 12                          
 15                          
 16                          
 20                          

[StefanKarpinski]

Can we please stop making up mathematical interpretations of arrays of arrays in a completely ad hoc manner and making a pastiche of incoherent behaviors based on these different interpretations? If we had a single, official "meaning" of an array of arrays and derived everything from that, great. But we do not and instead each person seems to pull a meaning out of thin air any time they want to.

[jebej]

I'm not sure that there are that many interpretations, the only two I've seen here are: 1. block matrices/vectors in which case flattening the array of arrays should give the non-blocked representation, or 2. vector spaces over array elements. Are there other interpretations?

[StefanKarpinski]

Those are the main ones but I feel like there have been additional variations in the presence of complex numbers. In any case, waffling between two is bad enough! I'm not trying to pick on you—it's an ongoing, pre-existing problem 😬

[rapus95]

How about creating and tagging an array-of-arrays label (for future progress at the meaning of them) and closing this?