# Avoiding allocations in jacobian system
**URL:** https://discourse.julialang.org/t/avoiding-allocations-in-jacobian-system/126376
**Category:** Performance
**Tags:** question, staticarrays
**Created:** [February 27, 2025, 9:39am UTC](https://discourse.julialang.org/t/avoiding-allocations-in-jacobian-system/126376 "2025-02-27T09:39:50Z")
**Posts on this page:** 3
**Page:** 1
### Author:  [@AP9](https://discourse.julialang.org/u/AP9)
#### Post date: [February 27, 2025, 9:39am UTC](https://discourse.julialang.org/t/avoiding-allocations-in-jacobian-system/126376/1 "2025-02-27T09:39:50Z")
Why is the below function allocating, and how can I optimize it so it does not allocate?
```julia
β = 100
S(x) = 1/(1+exp(-β*x))
S_prime(x) = β*S(x)*(1-S(x))
function jacobian_system(u, p, n)
ω, ω_A, A = p
x, y, s = u
return @SMatrix [
1 - 3x^2 - y^2 + S_prime(x) ω - 2x*y -A * ω_A * cos(ω_A * s)
-ω - 2x*y 1 - x^2 - 3y^2 0
0 0 0
]
end
test_u = [0.5, -1.7, 100.0]
test_p = [2pi, 2pi, 10.]
@btime jacobian_system(test_u, test_p, 3)
```
Output:
```julia
1.758 μs (20 allocations: 448 bytes)
```
By not including S\_prime(x) the output is:
```julia
59.299 ns (1 allocation: 80 bytes)
```
---
### Author:  [@gdalle](https://discourse.julialang.org/u/gdalle)
#### Post date: [February 27, 2025, 10:21am UTC](https://discourse.julialang.org/t/avoiding-allocations-in-jacobian-system/126376/2 "2025-02-27T10:21:41Z")
This is probably a benchmarking artefact due to the use of globals. It should disappear when you [interpolate](https://juliaci.github.io/BenchmarkTools.jl/dev/manual/#Interpolating-values-into-benchmark-expressions) these variables into `@btime`
---
### Author:  [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)
#### Post date: [February 27, 2025, 10:26am UTC](https://discourse.julialang.org/t/avoiding-allocations-in-jacobian-system/126376/3 "2025-02-27T10:26:06Z")
> [@AP9](#):
>
> `β = 100`
This is a global variable, not only for benchmarking.