Added support for kron

[JATippit]

Currently using kron with CuArrays returns a warning about scalar indexing. Added a kernel for kron with accompanying higher level function.

[codecov[bot]]

Codecov Report

Merging #814 (694039f) into master (4e81f3d) will decrease coverage by 0.38%. The diff coverage is 0.00%.

@@            Coverage Diff             @@
##           master     #814      +/-   ##
==========================================
- Coverage   78.03%   77.64%   -0.39%     
==========================================
  Files         120      121       +1     
  Lines        7383     7420      +37     
==========================================
  Hits         5761     5761              
- Misses       1622     1659      +37     

Impacted Files	Coverage Δ
src/CUDA.jl	100.00% <ø> (ø)
src/kronecker.jl	0.00% <0.00%> (ø)

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[mcabbott]

Is this quicker than just reshaping and broadcasting, with something like this?

function kron2d(A, B)
    A4 = reshape(A, 1, size(A,1), 1, size(A,2))
    B4 = reshape(B, size(B,1), 1, size(B,2), 1)
    C4 = A4 .* B4
    C = reshape(C4, size(A,1) * size(B,1), size(A,2) * size(B,2))
end

A = [1 2 3 4; 5 6 7 8]; B =  [1 10; 100 1000];
kron(A,B) == kron2d(A,B)

[JATippit]

Is this quicker than just reshaping and broadcasting, with something like this?

function kron2d(A, B)
    A4 = reshape(A, 1, size(A,1), 1, size(A,2))
    B4 = reshape(B, size(B,1), 1, size(B,2), 1)
    C4 = A4 .* B4
    C = reshape(C4, size(A,1) * size(B,1), size(A,2) * size(B,2))
end

A = [1 2 3 4; 5 6 7 8]; B =  [1 10; 100 1000];
kron(A,B) == kron2d(A,B)

Your function actually executes faster on my machine.

[maleadt]

Your function actually executes faster on my machine.

A custom kernel seems unnecessary then?

[JATippit]

Your function actually executes faster on my machine.

A custom kernel seems unnecessary then?

I agree - honestly didn't know reshape would work this way.

[maleadt]

Even though we don't need a custom kernel, we'd still need to provide kron with that implementation, so this didn't have to be closed.

[JATippit]

Would this be better added to a pre-existing file versus a standalone kronecker.jl then?

[mcabbott]

I agree - honestly didn't know reshape would work this way.

You may be interested in TensorCast.jl, my package for taking this seriously.

It's possible that some broadcasting implementation should be in Base, with the present implementation (with explicit loops) limited to Array or something -- it still seems faster on small CPU arrays. Not a short-term solution, of course. I think it would also solve https://github.com/JuliaLang/julia/issues/40439.