# Julia vs NumPy broadcasting

**URL:** <https://discourse.julialang.org/t/julia-vs-numpy-broadcasting/130908>\
**Category:** New to Julia\
**Created:** [July 21, 2025, 2:09pm UTC](https://discourse.julialang.org/t/julia-vs-numpy-broadcasting/130908 "2025-07-21T14:09:05Z")\
**Posts on this page:** 1\
**Showing post:** 13

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**Author:** ![mcabbott](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mcabbott/32/6603_2.png) [@mcabbott](https://discourse.julialang.org/u/mcabbott)\
**Post date:** [July 21, 2025, 6:08pm UTC](https://discourse.julialang.org/t/julia-vs-numpy-broadcasting/130908/13 "2025-07-21T18:08:28Z")

</div>

Do we need batched matrix multiplication? At least if @mikmoore 's version is correct, the loop is doing repeated matrix-vector multiplication `x[a, j] = V[a,b] * yj[b]` in a loop over `j`, whose batched version is matrix-matrix multiplication, `x[a, j] = V[a,b] * ys[b, j]`. For me that’s 20x quicker:

```julia
function step_reference3(A::Matrix, B::Vector, F::Real, n::Int) # my adaptation of @mikmoore's version
    λ, V = eigen(A)
    BF_transformed = V \ (B * F) # 4-element Vector{Float64}
    ys = expm1.(λ .* (1:n)') ./ λ .* BF_transformed
    x = V * ys # x[a, j] = V[a,b] * ys[b, j]
end

@btime step_reference($A, $B, $F, $n) # 2.602 ms (58011 allocations: 3.29 MiB)
@btime step_reference2($A, $B, $F, $n) # 3.401 ms (45033 allocations: 2.22 MiB)
@btime step_reference3($A, $B, $F, $n) # 155.708 μs (41 allocations: 326.47 KiB)

```

While loops are quick in Julia, loops which allocate small vectors are expensive. (The above SMatrix version didn’t run for me, on a quick attempt.)

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