# Loops with arrays of arbitrary dimensions
**URL:** https://discourse.julialang.org/t/loops-with-arrays-of-arbitrary-dimensions/60890
**Category:** General Usage
**Tags:** indexing, arrays
**Created:** [May 10, 2021, 1:52pm UTC](https://discourse.julialang.org/t/loops-with-arrays-of-arbitrary-dimensions/60890 "2021-05-10T13:52:46Z")
**Posts on this page:** 11
**Page:** 1
### Author:  [@fedoroff](https://discourse.julialang.org/u/fedoroff)
#### Post date: [May 10, 2021, 1:52pm UTC](https://discourse.julialang.org/t/loops-with-arrays-of-arbitrary-dimensions/60890/1 "2021-05-10T13:52:46Z")
Assume that I have a 2D array `A` and I want to do something like this
```julia
N1, N2 = 4, 3
A = ones((N1, N2))
x = zeros(N1)
for i2=1:N2
for i1=1:N1
x[i1] = 2 * A[i1, i2]
end
end
x = zeros(N2)
for i1=1:N1
for i2=1:N2
x[i2] = 2 * A[i1, i2]
end
end
```
Then, in case of 3D array `A` I will need to add one extra loop:
```julia
N1, N2, N3 = 4, 3, 2
A = ones((N1, N2, N3))
x = zeros(N1)
for i3=1:N3
for i2=1:N2
for i1=1:N1
x[i1] = 2 * A[i1, i2, i3]
end
end
end
# etc.
```
Now let’s assume I have an n-dimensional array `A`, and I want to specify some axis `ax` along which I want to multiply `A` by 2 and put the result to `x` (similarly to the above examples). The corresponding pseudo code can look like
```julia
ax = m
A = zeros((N1, N2, ..., Nn))
x = zeros(Nm)
for in=1:Nn
for i(n-1)=1:N(n-1)
...
for i(m+1)=1:N(m+1)
for i(m-1)=1:N(m-1)
...
for i2=1:N2
for i1=1:N1
for im=1:Nm
x[im] = 2 * A[i1, i2, ..., i(m-1), im, i(m+1), ..., i(n-1), in]
end
end
end
...
end
end
...
end
end
```
However, I want a generic code which will not depend on the number of `A` dimensions, i.e. some function `foo(x, A, ax)` which will do what I want independently of the size of `A`. How I should write such kind of code with loops for arbitrary dimension of `A`?
So far I found only [this](http://mikeinnes.github.io/2017/08/24/cudanative.html) old blog post which proposes to use macros. Did something changed since then? Can the corresponding loops be written with `ndims` and `axes` functions without macro?
---
### Author:  [@pdeffebach](https://discourse.julialang.org/u/pdeffebach)
#### Post date: [May 10, 2021, 1:56pm UTC](https://discourse.julialang.org/t/loops-with-arrays-of-arbitrary-dimensions/60890/2 "2021-05-10T13:56:13Z")
You are looking for `CartisianIndices`
```julia
julia> x2 = rand(2, 2);
julia> x3 = rand(2, 2, 2);
julia> for c in CartesianIndices(x2)
@show x2[c]
end
x2[c] = 0.4108577974629497
x2[c] = 0.4591618516787277
x2[c] = 0.22742754395597542
x2[c] = 0.9850643176704423
julia> for c in CartesianIndices(x3)
@show x3[c]
end
x3[c] = 0.2229783161443213
x3[c] = 0.4984591608388653
x3[c] = 0.4418623143086191
x3[c] = 0.6718510628390104
x3[c] = 0.21610541455088628
x3[c] = 0.574532213871789
x3[c] = 0.02381508624762918
x3[c] = 0.9172113813322624
```
---
### Author:  [@gdkrmr](https://discourse.julialang.org/u/gdkrmr)
#### Post date: [May 10, 2021, 2:04pm UTC](https://discourse.julialang.org/t/loops-with-arrays-of-arbitrary-dimensions/60890/3 "2021-05-10T14:04:49Z")
There is also `@nloops` [1]
[1] [Base.Cartesian · The Julia Language](https://docs.julialang.org/en/v1/devdocs/cartesian/#Base.Cartesian.@nloops)
---
### Author:  [@fedoroff](https://discourse.julialang.org/u/fedoroff)
#### Post date: [May 10, 2021, 2:24pm UTC](https://discourse.julialang.org/t/loops-with-arrays-of-arbitrary-dimensions/60890/4 "2021-05-10T14:24:51Z")
Can you please give me an example how I can write, let say, the following loop in terms of CartesianIndices:
```julia
N1, N2 = 4, 3
A = ones((N1, N2))
x = zeros(N1)
for i2=1:N2
for i1=1:N1
x[i1] = 2 * A[i1, i2]
end
end
```
`CartesianIndices(A)` and `CartesianIndices(x)` have different dimensions.
---
### Author:  [@pdeffebach](https://discourse.julialang.org/u/pdeffebach)
#### Post date: [May 10, 2021, 2:27pm UTC](https://discourse.julialang.org/t/loops-with-arrays-of-arbitrary-dimensions/60890/5 "2021-05-10T14:27:17Z")
> [@fedoroff](#):
>
> ```julia
> N1, N2 = 4, 3
> A = ones((N1, N2))
>
> x = zeros(N1)
> for i2=1:N2
> for i1=1:N1
> x[i1] = 2 * A[i1, i2]
> end
> end
>
> ```
I think this might be an XY problem. In the example above, you are overwriting `x` many times. Do you mean to have a `+=` intead of an `=`?
---
### Author:  [@jipolanco](https://discourse.julialang.org/u/jipolanco)
#### Post date: [May 10, 2021, 2:36pm UTC](https://discourse.julialang.org/t/loops-with-arrays-of-arbitrary-dimensions/60890/6 "2021-05-10T14:36:14Z")
Assuming this is what you want to do, you would write it like this:
```julia
for I in CartesianIndices(A)
i1 = I[1]
x[i1] = 2 * A[I]
end
```
---
### Author:  [@fedoroff](https://discourse.julialang.org/u/fedoroff)
#### Post date: [May 10, 2021, 3:29pm UTC](https://discourse.julialang.org/t/loops-with-arrays-of-arbitrary-dimensions/60890/7 "2021-05-10T15:29:02Z")
Its just a fake example which came to my mind. It can be either of them.
---
### Author:  [@pdeffebach](https://discourse.julialang.org/u/pdeffebach)
#### Post date: [May 10, 2021, 3:30pm UTC](https://discourse.julialang.org/t/loops-with-arrays-of-arbitrary-dimensions/60890/8 "2021-05-10T15:30:00Z")
Then @jipolanco 's solution above is what you want.
---
### Author:  [@fedoroff](https://discourse.julialang.org/u/fedoroff)
#### Post date: [May 10, 2021, 3:30pm UTC](https://discourse.julialang.org/t/loops-with-arrays-of-arbitrary-dimensions/60890/9 "2021-05-10T15:30:29Z")
Thank you. Seems like what I need.
Just a small question. Why do I need to take Tuple of I? It seems to work with just I[1].
---
### Author:  [@jipolanco](https://discourse.julialang.org/u/jipolanco)
#### Post date: [May 10, 2021, 3:44pm UTC](https://discourse.julialang.org/t/loops-with-arrays-of-arbitrary-dimensions/60890/10 "2021-05-10T15:44:43Z")
Oops, you’re totally right about that! I wasn’t sure that it worked.
---
### Author:  [@fedoroff](https://discourse.julialang.org/u/fedoroff)
#### Post date: [May 10, 2021, 3:51pm UTC](https://discourse.julialang.org/t/loops-with-arrays-of-arbitrary-dimensions/60890/11 "2021-05-10T15:51:15Z")
Thank you all guys for the help.