# Speed up parallel maximum across columns

**URL:** <https://discourse.julialang.org/t/speed-up-parallel-maximum-across-columns/45006>\
**Category:** Performance\
**Tags:** parallel, distributed, loops\
**Created:** [August 15, 2020, 6:42pm UTC](https://discourse.julialang.org/t/speed-up-parallel-maximum-across-columns/45006 "2020-08-15T18:42:54Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![fyang](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fyang/32/17228_2.png) [@fyang](https://discourse.julialang.org/u/fyang)\
**Post date:** [August 15, 2020, 6:42pm UTC](https://discourse.julialang.org/t/speed-up-parallel-maximum-across-columns/45006/1 "2020-08-15T18:42:54Z")

</div>

Hi Julia community!

I need help on speeding up a function with parallelization. Here’s a MWE.

```julia
using Distributed; n_cores = 3; addprocs(n_cores)
@everywhere using SharedArrays, BenchmarkTools
M = 10000; N = 10000; k = 2; mu = rand(N, 1)
U1 = SharedArray{Float32}(rand(M, N))
U2 = SharedArray{Float32}(rand(M, N))
idv_d = SharedArray{Float32}(N, M)
d = SharedArray{Float32}(M, 1)
function get_d!(U1, U2, mu, k, d, idv_d)
    fill!(idv_d, 0.0)
    @inbounds @sync @distributed for j in 1:N
        u_1, arg_1 = findmax(@view U1[:, j])
        u_2, arg_2 = findmax(@view U2[:, j])
        if u_1 >= u_2
            idv_d[j, arg_1] = mu[j]
        else
            idv_d[j, arg_2] = mu[j] ./ k
        end
    end
    @inbounds @sync @distributed for j in 1:M
        d[j] = sum(idv_d[:, j])
    end
end
@btime get_d!(U1, U2, mu, k, d, idv_d)

```

`M` and `N` will be two large numbers (on the order of 10^6), and I intend to run this on clusters so `n_cores` will be about 50-100. The function calculates aggregate demand given two utility matrices (`U1`, `U2`). The only output that I’m interested in is `d` not `idv_d`, but I don’t see a fast way to get `d` with parallelization without calculating `idv_d` first.

I have tried to optimize the code for a while and this is the best I can come up with. I noticed that looping over columns helps a lot. However, I wonder whether I’m leaving some performance on the table. Are there any ways to speed this up? I have no concerns about readability. Would really appreciate any help!

---

<div class="post-metadata">

**Author:** ![fyang](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fyang/32/17228_2.png) [@fyang](https://discourse.julialang.org/u/fyang)\
**Post date:** [August 18, 2020, 7:06pm UTC](https://discourse.julialang.org/t/speed-up-parallel-maximum-across-columns/45006/2 "2020-08-18T19:06:42Z")

</div>

Update: I spent a bit more time on the code. Running the above in Julia v1.3.1 on my macbook gives

```nohighlight
  308.112 ms (1440 allocations: 70.05 KiB)

```

I changed where I put @views and got ~20% reduction on runtime.

```nohighlight
function get_d_v2!(U1, U2, mu, k, d, idv_d)
    fill!(idv_d, 0.0)
    @inbounds @sync @distributed for j in 1:N
        u_1, arg_1 = @views findmax(U1[:, j])
        u_2, arg_2 = @views findmax(U2[:, j])
        if u_1 >= u_2
            idv_d[j, arg_1] = mu[j]
        else
            idv_d[j, arg_2] = mu[j] / k
        end
    end
    @inbounds @sync @distributed for j in 1:M
        d[j] = @views sum(idv_d[:, j])
    end
end
@btime get_d_v2!(U1, U2, mu, k, d, idv_d)

```

```nohighlight
  255.680 ms (1439 allocations: 70.06 KiB)

```