Here I'll discuss a variety of Matrix-vector operations, naturally starting with matrix-vector multiplication.
function jgemvavx!(𝐲, 𝐀, 𝐱) @avx for i ∈ eachindex(𝐲) 𝐲i = zero(eltype(𝐲)) for j ∈ eachindex(𝐱) 𝐲i += 𝐀[i,j] * 𝐱[j] end 𝐲[i] = 𝐲i end end
Using a square
𝐀, we find the following results.
𝐀 is transposed, or equivalently, if we're instead computing
x * 𝐀:
Finally, the three-argument dot product
y' * 𝐀 * x:
The performance impact of alignment is dramatic here.