# Matrix-Vector multiplication complex/real

**URL:** <https://discourse.julialang.org/t/matrix-vector-multiplication-complex-real/57129>\
**Category:** Performance\
**Created:** [March 14, 2021, 1:53pm UTC](https://discourse.julialang.org/t/matrix-vector-multiplication-complex-real/57129 "2021-03-14T13:53:18Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![jamblejoe](https://avatars.discourse-cdn.com/v4/letter/j/ee7513/32.png) [@jamblejoe](https://discourse.julialang.org/u/jamblejoe)\
**Post date:** [March 14, 2021, 1:53pm UTC](https://discourse.julialang.org/t/matrix-vector-multiplication-complex-real/57129/1 "2021-03-14T13:53:18Z")

</div>

The functions executed for `A*y` are different for `A` either real or complex.The first code uses BLAS `gemv!` (checked via `@code_native`)

```julia
A = rand(ComplexF64, n, n)
y = rand(Float64, n)
c = Vector{Complex64}(undef, n)

mul!(c,A,y)

n=20000
julia> @btime mul!($c, $A, $y)
  254.250 ms (0 allocations: 0 bytes)

```

while

```julia
A = rand(Float64, n, n)
y = rand(ComplexF64, n)
c = Vector{Complex64}(undef, n)

mul!(c,A,y)

n=20000
julia> @btime mul!($c, $A, $y)
  271.984 ms (0 allocations: 0 bytes)

julia> BLAS.set_num_threads(1)

julia> @btime mul!($c, $A, $y)
  276.834 ms (0 allocations: 0 bytes)

```

uses `generic_matvecmul!`. The performance for `n=20000` and 4 threads, is still similar. But BLAS is multithreaded, while `generic_matvecmul!` isnt. I can not check how both cases scale for larger `n` and more threads right now.

I am interested in the latter case and wonder why it is not using BLAS and is not multithreaded? I thought `generic_` functions are fallbacks in Julia and one should look for specialized functions when one is interested in performance.

Could someone give some insights in this?