Matrix-Vector Operations

Here I'll discuss a variety of Matrix-vector operations, naturally starting with matrix-vector multiplication.

function jgemvavx!(𝐲, 𝐀, 𝐱)
    @turbo 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 Size x Size matrix 𝐀, we find the following results.

If 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.