# Is it possible to name slices of arrays as functions?

**URL:** <https://discourse.julialang.org/t/is-it-possible-to-name-slices-of-arrays-as-functions/36934>\
**Category:** New to Julia\
**Created:** [April 3, 2020, 2:36am UTC](https://discourse.julialang.org/t/is-it-possible-to-name-slices-of-arrays-as-functions/36934 "2020-04-03T02:36:10Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![peterj](https://avatars.discourse-cdn.com/v4/letter/p/22d042/32.png) [@peterj](https://discourse.julialang.org/u/peterj)\
**Post date:** [April 3, 2020, 2:36am UTC](https://discourse.julialang.org/t/is-it-possible-to-name-slices-of-arrays-as-functions/36934/1 "2020-04-03T02:36:10Z")

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A common use case for me, and lots of people I would think, is to have large systems of DEs such as

dx\_i / dt = …  
dy\_i / dt = …

where i \in [1, n] and x\_i, y\_i represents the ith class of x, y respectively.

Usually I define the state in these ODEs as one big vector of length 2n, like

```julia
const n = 100 #some number of dimensions
system_state = zeros(2*n)
system_state[1:n] #these are the x_i
 
system_state[n+1:2*n] #these are the y_i

```

Then the ODE function is something like this, with all the operations broadcasted

```julia
function f(du,u,p,t)
     x = @view u[1:n]
     y = @view u[n+1:2*n]
     du[1:n] .= -1 .* x
     du[n+1:2*n] .= x .* y
end

```

This works, but I end up having lots of slices around my code, which can be difficult to read.  
I was hoping there was a zero-cost way of writing a shorthand function like

```julia
x(state) = @view state[1:n]

```

which I can then use to modify the state exactly like the original slice. However this doesn’t seem to work, I get the error “invalid assignment location”.

Is there a way to do this in Julia?

Thanks

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<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [April 3, 2020, 2:44am UTC](https://discourse.julialang.org/t/is-it-possible-to-name-slices-of-arrays-as-functions/36934/2 "2020-04-03T02:44:51Z")

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> [@peterj](#):
>
> This works, but I end up having lots of slices around my code, which can be difficult to read.  
> I was hoping there was a zero-cost way of writing a shorthand function like

> **[GitHub - SciML/LabelledArrays.jl: Arrays which also have a label for each...](https://github.com/SciML/LabelledArrays.jl)**
>
> Arrays which also have a label for each element for easy scientific machine learning (SciML) - GitHub - SciML/LabelledArrays.jl: Arrays which also have a label for each element for easy scientific ...

```julia
using LabelledArrays
julia> z = @LArray [1 2; 3 4] (a = (2, :), b = 2:3);
julia> z.a
2-element view(::Array{Int64,2}, 2, :) with eltype Int64:
 3
 4

```

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<div class="post-metadata">

**Author:** ![peterj](https://avatars.discourse-cdn.com/v4/letter/p/22d042/32.png) [@peterj](https://discourse.julialang.org/u/peterj)\
**Post date:** [April 3, 2020, 3:36am UTC](https://discourse.julialang.org/t/is-it-possible-to-name-slices-of-arrays-as-functions/36934/3 "2020-04-03T03:36:30Z")

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Cool, thanks!

---

<div class="post-metadata">

**Author:** ![peterj](https://avatars.discourse-cdn.com/v4/letter/p/22d042/32.png) [@peterj](https://discourse.julialang.org/u/peterj)\
**Post date:** [April 3, 2020, 5:37am UTC](https://discourse.julialang.org/t/is-it-possible-to-name-slices-of-arrays-as-functions/36934/4 "2020-04-03T05:37:13Z")

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I have a quick question related to the use of labelledarrays in this way.  
My current toy example is

```julia

function f(du,u,p,t)
    x = @view u[1:n]
    y = @view u[n+1:2*n]
    du[1:n] .= -1 .* x
    du[n+1:2*n] .= -1 .* y
end
const n = 10
u_0 = @LArray fill(1.0,2*n) (x = (1:n),y = (n+1:2*n))
prob = ODEProblem(f,u_0,(0,10.0),[])
sol = solve(prob,Tsit5())

```

Is it possible to define a custom type of labelledarray, like say `state_type = LArray{2*n}(x = (1:n),y = (n+1:2*n))`, so I can easily specify function signatures that return labelled arrays with the format of u\_0? I’ve tried a few different things and none of them worked.

Let me know if this should be asked as a new topic or not as well.

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<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [April 3, 2020, 5:38am UTC](https://discourse.julialang.org/t/is-it-possible-to-name-slices-of-arrays-as-functions/36934/5 "2020-04-03T05:38:47Z")

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I am not sure of a good way to implement that well.

---

<div class="post-metadata">

**Author:** ![peterj](https://avatars.discourse-cdn.com/v4/letter/p/22d042/32.png) [@peterj](https://discourse.julialang.org/u/peterj)\
**Post date:** [April 3, 2020, 5:49am UTC](https://discourse.julialang.org/t/is-it-possible-to-name-slices-of-arrays-as-functions/36934/6 "2020-04-03T05:49:29Z")

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Thanks for the fast reply.

I was benchmarking this code and found that the LabelledArrays one is actually slightly faster, although I’m not sure why they are allocating so much.

```julia
using DifferentialEquations
using LabelledArrays

function f1(du,u,p,t)
    x = @view u[1:n]
    y = @view u[n+1:2*n]
    du[1:n] .= -1 .* x .* u.y
    du[n+1:2*n] .= -1 .* y
end
function f2(du,u,p,t)
    du.x .= -1 .* u.x .* u.y
    du.y .= -1 .* u.y
end
const n = 1000
using BenchmarkTools
u_0 = @LArray fill(1000.0,2*n) (x = (1:n),y = (n+1:2*n))
prob1 = ODEProblem(f1,u_0,(0,100.0),[])
@btime solve(prob1,Tsit5());

prob2 = ODEProblem(f2,u_0,(0,100.0),[])
@btime solve(prob2,Tsit5());

  31.841 ms (29417 allocations: 43.50 MiB)
  27.728 ms (29417 allocations: 43.50 MiB)

```