Best way to subtract Matrix from Vector of Matrix - julia

Question

I want to subtract a Matrix from a Vector of Matrix. For Example, In below defined variable i want to subtract y for each element of xl
xl = [Matrix{Float64}(undef, 2, 3) for i in 1:1000]
y = Matrix{Float64}(undef, 2, 3)
I know this can be done with map function
map(x -> x-y, xl)
But is there any better way to do this or can we reduce runtime by multithreading? I tried benchmarking simple map and ThreadsX.map and found ThreadsX.map is slower any suggestion to reduce runtime.
#btime map(x -> x-y, xl); # 55.558 μs (1010 allocations: 117.59 KiB)
#btime ThreadsX.map(x -> x-y, xl); # 99.764 μs (5414 allocations: 285.47 KiB)
Note: Here Matrix is just an example I want to do this on large vector of custom struct that support subtraction.

Answer 1

First of all, map is not the fastest thing, loops will almost always beat it. This array comprehension is 70% faster than map.
#btime [[x[i]-$y[i] for i in eachindex($y)] for x in $xl];
33.300 μs (1001 allocations: 117.31 KiB)
Now, for why multithreading is slower, the answer might be that multithreading setup for this simple calculation has non-negligible overhead. You want a heavier calculation for multithreading to have a noticeable effect. Also, don't forget to interpolate ($) when timing with #btime.
#btime map(x -> x-$y, $xl);
55.600 μs (1001 allocations: 117.31 KiB)
#btime $xl .- ($y,); # broadcasting
56.100 μs (1001 allocations: 117.31 KiB)
#btime ThreadsX.map(x -> x-$y, $xl);
53.600 μs (1602 allocations: 242.05 KiB)
See this heavier example, you get about 6X speedup with multithreading:
julia> #btime ThreadsX.map(x -> exp.(sin.(x))-exp.(sin.($y)), $xl);
303.700 μs (3605 allocations: 460.89 KiB)
julia> #btime map(x -> exp.(sin.(x))-exp.(sin.($y)), $xl);
1.673 ms (3001 allocations: 336.06 KiB)

Answer 2

By default, Julia start with just one thread. To start Julia with more than one thread you can use --threads=n option:
PS C:\Users\Elias> julia --threads=4
_
_ _ _(_)_ | Documentation: https://docs.julialang.org
(_) | (_) (_) |
_ _ _| |_ __ _ | Type "?" for help, "]?" for Pkg help.
| | | | | | |/ _` | |
| | |_| | | | (_| | | Version 1.7.2 (2022-02-06)
_/ |\__'_|_|_|\__'_| | Official https://julialang.org/ release
|__/ |
julia> xl = [rand(2, 3) for i in 1:1000];
julia> y = rand(2, 3);
julia> using ThreadsX
julia> using BenchmarkTools
julia> #btime ThreadsX.map(x -> x-$y, $xl);
42.700 μs (1353 allocations: 206.77 KiB)
For more details, see: https://docs.julialang.org/en/v1/manual/multi-threading/