# Differentiable vectorized piecewise function in Julia?
**URL:** https://discourse.julialang.org/t/differentiable-vectorized-piecewise-function-in-julia/73766
**Category:** General Usage
**Created:** [December 29, 2021, 5:00pm UTC](https://discourse.julialang.org/t/differentiable-vectorized-piecewise-function-in-julia/73766 "2021-12-29T17:00:38Z")
**Posts on this page:** 7
**Page:** 1
### Author:  [@DeepQ](https://discourse.julialang.org/u/DeepQ)
#### Post date: [December 29, 2021, 5:00pm UTC](https://discourse.julialang.org/t/differentiable-vectorized-piecewise-function-in-julia/73766/1 "2021-12-29T17:00:38Z")
How could I define this function in Julia?
f(x) = \begin{cases} x^2 &\text {x \< 2} \\ (x-2)(x-4) &\text {otherwise}\end{cases}
---
### Author:  [@lrnv](https://discourse.julialang.org/u/lrnv)
#### Post date: [December 29, 2021, 5:01pm UTC](https://discourse.julialang.org/t/differentiable-vectorized-piecewise-function-in-julia/73766/2 "2021-12-29T17:01:55Z")
```julia
function f(x)
if x < 2
return x^2
else
return (x-2)*(x-4)
end
end
```
?
---
### Author:  [@DeepQ](https://discourse.julialang.org/u/DeepQ)
#### Post date: [December 29, 2021, 5:29pm UTC](https://discourse.julialang.org/t/differentiable-vectorized-piecewise-function-in-julia/73766/3 "2021-12-29T17:29:02Z")
Thank you. But I said vectorized and differentiable. Its input must be a vector or matrix.
---
### Author:  [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)
#### Post date: [December 29, 2021, 5:37pm UTC](https://discourse.julialang.org/t/differentiable-vectorized-piecewise-function-in-julia/73766/4 "2021-12-29T17:37:06Z")
Linking [related thread](https://discourse.julialang.org/t/performant-piecewise-function-evaluation/45762/4) that seems to address the differentiable part.
As for the vectorization, `f.(x)` should work above?
---
### Author:  [@machineko](https://discourse.julialang.org/u/machineko)
#### Post date: [December 29, 2021, 5:43pm UTC](https://discourse.julialang.org/t/differentiable-vectorized-piecewise-function-in-julia/73766/5 "2021-12-29T17:43:14Z")
just add . to make it working on mult-dim data (or just use f.())
```julia
using Zygote
function f(x)
if all(x .< 2)
return x.^2
else
return (x.-2).*(x.-4)
end
end
jacobian(f, [1.0, 2.0, 3.0])
```
---
### Author:  [@lrnv](https://discourse.julialang.org/u/lrnv)
#### Post date: [December 29, 2021, 5:44pm UTC](https://discourse.julialang.org/t/differentiable-vectorized-piecewise-function-in-julia/73766/6 "2021-12-29T17:44:12Z")
I do not understand what you want. For me this is ok :
```julia
julia> function f(x)
if x < 2
return x^2
else
return (x-2)*(x-4)
end
end
f (generic function with 1 method)
julia> x = [1,2,3]
3-element Vector{Int64}:
1
2
3
julia> f.(x)
3-element Vector{Int64}:
1
0
-1
julia> using ForwardDiff
julia> ForwardDiff.derivative.(f,x)
3-element Vector{Int64}:
2
-2
0
julia>
```
---
### Author:  [@lrnv](https://discourse.julialang.org/u/lrnv)
#### Post date: [December 29, 2021, 5:47pm UTC](https://discourse.julialang.org/t/differentiable-vectorized-piecewise-function-in-julia/73766/7 "2021-12-29T17:47:57Z")
> [@DeepQ](#):
>
> Its input must be a vector or matrix.
This is unclear to me, as the condition “x \> 2” is undefined for a vector or matrix.