# Grid of all elements of an arbitrarily sized matrix

**URL:** <https://discourse.julialang.org/t/grid-of-all-elements-of-an-arbitrarily-sized-matrix/89024>\
**Category:** General Usage\
**Tags:** iterators\
**Created:** [October 20, 2022, 4:58pm UTC](https://discourse.julialang.org/t/grid-of-all-elements-of-an-arbitrarily-sized-matrix/89024 "2022-10-20T16:58:13Z")\
**Posts on this page:** 8\
**Page:** 1

<div class="post-metadata">

**Author:** ![CeterisPartybus](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ceterispartybus/32/46868_2.png) [@CeterisPartybus](https://discourse.julialang.org/u/CeterisPartybus)\
**Post date:** [October 20, 2022, 4:58pm UTC](https://discourse.julialang.org/t/grid-of-all-elements-of-an-arbitrarily-sized-matrix/89024/1 "2022-10-20T16:58:13Z")

</div>

I have an `n*m` sized array `A`, and I would like to create a grid of its elements. The output should look something like:

```
B = (A[1,1], A[2,1]
     A[1,1], A[2,2]
     ...
     A[1,1], A[2,m]
     A[1,2], A[2,1]
     A[1,2], A[2,2]
     ...
     A[1,2], A[2,m]
     ...
     A[n,1], A[n,m])

```

My first approach would be to do something like this:

```
A = [1 5;
     2 6;
     3 7;
     4 8]

B = collect(Iterators.product(A))

```

However, this only returns

```
4×2 Matrix{Tuple{Int64}}:
 (1,) (5,)
 (2,) (6,)
 (3,) (7,)
 (4,) (8,)

```

Instead of the desired output above.

Any ideas?

---

<div class="post-metadata">

**Author:** ![DNF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dnf/32/10191_2.png) [@DNF](https://discourse.julialang.org/u/DNF)\
**Post date:** [October 20, 2022, 5:15pm UTC](https://discourse.julialang.org/t/grid-of-all-elements-of-an-arbitrarily-sized-matrix/89024/3 "2022-10-20T17:15:38Z")

</div>

I guess you want something along the lines of

```julia
julia> Iterators.product(A[:, 1], A[:, 2]) |> collect
4×4 Matrix{Tuple{Int64, Int64}}:
 (1, 5) (1, 6) (1, 7) (1, 8)
 (2, 5) (2, 6) (2, 7) (2, 8)
 (3, 5) (3, 6) (3, 7) (3, 8)
 (4, 5) (4, 6) (4, 7) (4, 8)

```

Tweak shape etc. as needed.

---

<div class="post-metadata">

**Author:** ![CeterisPartybus](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ceterispartybus/32/46868_2.png) [@CeterisPartybus](https://discourse.julialang.org/u/CeterisPartybus)\
**Post date:** [October 20, 2022, 5:15pm UTC](https://discourse.julialang.org/t/grid-of-all-elements-of-an-arbitrarily-sized-matrix/89024/4 "2022-10-20T17:15:48Z")

</div>

Thanks for the suggestion. But this only reshapes the array. But what I need is a bit different.  
Let me give you an example:

```julia
A = [1 5;
     2 6;
     3 7;
     4 8]

```

And the result should be:

```julia
B = [1 5;
     1 6;
     1 7;
     1 8;
     2 5;
     2 6;
     2 7;
     2 8;
     3 5;
     3 6;
     3 7;
     3 8;
     4 5;
     4 6;
     4 7;
     4 8;]

```

I could write it in a nested loop but it should be able to handle arrays of any `n*m`.  
The `Iterator.product()` function is promising but I do not know how to get it to work with a matrix. It does work with separate vectors though. And I don’t know how to make it work without inputting a fixed amount of vectors.

---

<div class="post-metadata">

**Author:** ![CeterisPartybus](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ceterispartybus/32/46868_2.png) [@CeterisPartybus](https://discourse.julialang.org/u/CeterisPartybus)\
**Post date:** [October 20, 2022, 5:18pm UTC](https://discourse.julialang.org/t/grid-of-all-elements-of-an-arbitrarily-sized-matrix/89024/5 "2022-10-20T17:18:08Z")

</div>

Thanks! That’s what I also thought. I just need to be able to make the

```julia
A[:, 1], A[:, 2]

```

flexible. So, I need to be able to input a matrix with any number of columns.

---

<div class="post-metadata">

**Author:** ![DNF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dnf/32/10191_2.png) [@DNF](https://discourse.julialang.org/u/DNF)\
**Post date:** [October 20, 2022, 5:21pm UTC](https://discourse.julialang.org/t/grid-of-all-elements-of-an-arbitrarily-sized-matrix/89024/6 "2022-10-20T17:21:31Z")

</div>

This should work, though I’m unsure if it is efficient:

```julia
Iterators.product(eachcol(A)...) |> collect

```

If you want one tall vector, just pass it into `vec`:

```julia
Iterators.product(eachcol(A)...) |> collect |> vec

```

---

<div class="post-metadata">

**Author:** ![CeterisPartybus](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ceterispartybus/32/46868_2.png) [@CeterisPartybus](https://discourse.julialang.org/u/CeterisPartybus)\
**Post date:** [October 20, 2022, 5:24pm UTC](https://discourse.julialang.org/t/grid-of-all-elements-of-an-arbitrarily-sized-matrix/89024/7 "2022-10-20T17:24:36Z")

</div>

That works. Awesome, thanks!  
Can you just quickly explain what the three dots do?

Sorry, I just switched to Julia.

---

<div class="post-metadata">

**Author:** ![DNF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dnf/32/10191_2.png) [@DNF](https://discourse.julialang.org/u/DNF)\
**Post date:** [October 20, 2022, 5:34pm UTC](https://discourse.julialang.org/t/grid-of-all-elements-of-an-arbitrarily-sized-matrix/89024/8 "2022-10-20T17:34:15Z")

</div>

The three dots, the _splatting operator_, unpacks a collection of elements into a list of arguments.

For example, if you have a function, `foo(x, y)` that takes two arguments, you cannot call it like this: `foo([1, 2])`. But you can unpack the elements from the array into two arguments: `foo([1, 2]...)`

You can read docstrings for operators and functions like this:

```julia
julia> ? # type question mark. The prompt turns into

help?> ... # type the operator you are wondering about, like ...
search: ...

  ...

  The "splat" operator, ..., represents a sequence of arguments. ... can be used  
  in function definitions, to indicate that the function accepts an arbitrary     
  number of arguments. ... can also be used to apply a function to a sequence of  
  arguments.

  Examples
  ≡≡≡≡≡≡≡≡≡≡

```

(The same syntax is used for “slurping”, which is sort of the opposite.)

---

<div class="post-metadata">

**Author:** ![CeterisPartybus](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ceterispartybus/32/46868_2.png) [@CeterisPartybus](https://discourse.julialang.org/u/CeterisPartybus)\
**Post date:** [October 20, 2022, 5:35pm UTC](https://discourse.julialang.org/t/grid-of-all-elements-of-an-arbitrarily-sized-matrix/89024/9 "2022-10-20T17:35:17Z")

</div>

That makes sense. Thanks!