Speed improvement [🇷 for BE/BA]

posted by PharmCat  – Russia, 2020-08-08 19:27 (2138 d 05:51 ago) – Posting: # 21840
Views: 36,320

❝ 30%...It ain't much but it's honest work. :-)


It is very good boost. I donn't know how matrix multipication works in R, but some improovments can be done if make function A = B'*C*B or A += B'*C*B. At each step of this function there are many intermediate products that can be avoided with direct computation. (Or make it in C)

Example incremantal function:

"""
A' * B * A -> +θ (cache)
A' * B * C -> +β
"""
function mulθβinc!(θ, β, A::AbstractMatrix, B::AbstractMatrix, C::Vector)
    q = size(B, 1)
    p = size(A, 2)
    c = zeros(eltype(B), q)
    for i = 1:p
        c .= 0
        for n = 1:q
            for m = 1:q
                @inbounds c[n] += B[m, n] * A[m, i]
            end
            @inbounds β[i] += c[n] * C[n]
        end
        for n = 1:p
            for m = 1:q
                @inbounds θ[i, n] += A[m, n] * c[m]
            end
        end
    end
    θ, β
end

function mulsimple!(θ, β, A::AbstractMatrix, B::AbstractMatrix, C::Vector)
    AB = A'*B
    θ .+ AB*A, β .+ AB*C
end

θ = zeros(4, 4)
β = zeros(4)

A = [1 3 4 3; 2 3 2 3; 3 4 5 6; 3 4 5 6] B = [1 3 4 3; 2 3 2 3; 3 4 5 6; 3 4 5 6] C = [1, 3, 4 ,3]

julia> @time mulsimple!(θ, β, A, B, C);
0.000007 seconds (10 allocations: 1.172 KiB)

julia> @time mulθβinc!(θ, β, A, B, C);
0.000004 seconds (2 allocations: 144 bytes)

eightfold memory savings

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