Zero-dimensional arrays FAQ

[cossio]

Adding some documentation about zero-dimensional arrays. Some discussion on Slack:

https://julialang.slack.com/archives/C6GHSTN4T/p1529875426000022

I copied/pasted some comments by more knowledgeable people, with minor edits.

Questions about 0-dimensional arrays arise often. And I think they are a bit unintuitive. Some documentation might help.

https://discourse.julialang.org/t/what-is-the-reason-for-a-zero-dimensional-array/7175

https://discourse.julialang.org/t/why-have-0-dimensional-arrays/797

Hopefully this clarifies the concept for others as well.

Supersedes #27765.

[StefanKarpinski]

Very nice write up!

[cossio]

Thanks to @mbauman , @nalimilan , @KristofferC

[nalimilan]

Break lines at 92 chars.

[cossio]

Done

[cossio]

Break long lines

[cossio]

Done

[cossio]

Done

[StefanKarpinski]

There are white space issues.

[cossio]

What exactly? What do I have to do?

[StefanKarpinski]

Run make check-whitespace and it will report that certain lines have trailing whitespace. Get rid of the trailing whitespace, get make check-whitespace passing and then push the fixed version.

[mbauman]

He's editing via GitHub, though, which does indeed make this difficult to see. It's not ideal, but we have this rule since many contributors' editors do automatically remove whitespace in any file they touch… leading to unrelated changes, conflicts, and churn.

[mbauman]

Now that this lives in a FAQ, let's make this a question.

[cossio]

Yep, I was editing in Github directly. Anyway I think I addressed the issues. Let me know if something else is needed.

[garrison]

I think this is a great write up. I do worry, though, that it makes zero-dimensional arrays seem too appealing, and that this may lead to people using them in places where an alternative might work better. For instance, in many cases, a Ref would communicate intent more clearly (as mentioned on Discourse). In short: I think this write up leaves out the following: why might one not want to use zero-dimensional arrays in a given circumstance? Do they exist mainly for conceptual completeness, or are there real-world use cases where they should be encouraged?

[mbauman]

Well, ideally Refs would also implement all the methods to make them behave largely like 0-dimensional arrays themselves (#26988). But, I think you're right — typically folks don't need or run into them, which is precisely why they cause confusion when it does occur, and which is why it's nice to have it as a FAQ instead of a part of the narrative manual. They do mostly just "fall out" of an implementation in a consistent manner; a good example is view(A, 1) which provides a view into the first element slot of an array. Returning an unwrapped scalar would no longer be a view. I'd wager they're most likely obtained by accidentally forgetting args in zeros() or Array{Int}(undef) or some such.

We could perhaps emphasize further the fact that 0-dimensional arrays are first and foremost containers and do not behave like the element they wrap. Furthermore, I had been also thinking about calling out the fact that we do not allow 0-dimensional arrays to participate in the linear algebra of matrices. Thus, while you can broadcast rand(3,3) .* fill(2), we have not defined the multiplication rand(3,3) * fill(2).

Just checking in here: how you doing, @cossio? Getting revision fatigue yet? Let us know before you get too frustrated with us. I know incremental reviews can be a challenge. :)

[cossio]

Doing fine @mbauman. Unfortunately I don't have the necessary knowledge to contribute much to this discussion.

[StefanKarpinski]

I think this is good as is. If someone wants to tweak the language to make zero-dimensional arrays sound less appealing after this is merged, they can do that. The new text addresses a common point of confusion well, so let's just merge it.

[cossio]

Why CI fails? I don't understand the error message:

!! 'Arrays' is not unique. [src/manual/mathematical-operations.md]

[fredrikekre]

I believe there is a clash between the header you are adding and some existing ## Arrays header in the manual. Lets wait for #27769 to resolve that.

[DrKrar]

I think A[1,1] would produce an error

[StefanKarpinski]

It doesn't:

julia> A = fill(1)
0-dimensional Array{Int64,0}:
1

julia> A[1,1]
1

Same rule that allows indexing a vector like an n×1 matrix (or n×1×1 three-tensor):

julia> v = rand(3)
3-element Array{Float64,1}:
 0.7636187688715259
 0.6218914012928478
 0.22322554192055066

julia> v[3,1]
0.22322554192055066

julia> v[3,1,1]
0.22322554192055066

[nalimilan]

Locally the build passes with that PR after rebasing on master (now that #27769 is merged).

[cossio]

@nalimilan Should I do something?

[nalimilan]

You could rebase on master and force-push so that CI is run again, but I don't think it's possible from GitHub, so we can just merge as-is.

[simonbyrne]

Thanks!

[cossio]

awesome!

[cossio]

@StefanKarpinski The bulleted list appears broken: https://docs.julialang.org/en/latest/manual/faq/#Arrays-1. I guess to fix that I would have to remove the line breaks in the source markdown, but that's agains the max-chars per line rule. How do I fix this?

[KristofferC]

This should fix it: #27840.

Seems that the markdown parser doesn't do a correct job here?

[cossio]

@KristofferC Thanks!

[andyferris]

Suggestion: "...(even though some scalar types such as Number are iterable..."

(I'm pretty sure broadcasting, map/reduce/filter of arrays of scalars, etc doesn't rely on this being defined for all scalar types?)