1D comprehensions with multiple variables

[kmsquire]

I just tried to do

julia> [(i,j) for i=1:5, j=i:5]
ERROR: i not defined
 in anonymous at no file

Unfortunately, this produces an error that i is undefined, since this produces a 2D array in Julia.

Related to discussion in #550, especially #550 (comment), but there, the proposal is to force 1D array creation in the presence of an if clause (which makes sense).

I'm not sure there's a good solution here, mainly because I don't know how popular/common the 2D comprehension syntax is.

[JeffBezanson]

I think the if clause solution is as reasonable as it's going to get. Reopen if a different idea occurs to you.

[RaulDurand]

What about the use of two for (a la Python ) in order to use the first variable?

L = [ i+j for i=1:10 for j=i:10 if (i+j)%2>0 ]    # returns a 1D array

See my comment #550 (comment)

[JeffBezanson]

Yeah that's a good idea.

[StefanKarpinski]

I'm not super keen on the double for thing – largely because the double for seems to me like the version that should produce a 2-d array. I proposed at some point that the presence of an if always flatten.

[nalimilan]

if i >= j could be useful if it created symmetric matrices. But TBH I'm not sure the complexity that would add is worth it.

[daviddelaat]

If the if syntax is implemented by growing an array (which is probably necessary for when there are a large number of iterations and the if statement is almost always false), then I think we need some other notation for getting the 1-d result.

I also think the if true syntax feels a bit hacky (and for me nested 1-d comprehensions are much more common than conditions in comprehensions).

I like @RaulDurand proposal, but the other way around is also possible: double for to get a matrix and comma's to vectorize.

[prcastro]

I like @daviddelaat proposal, feels much more natural than 2 fors for 1-D array.

[StefanKarpinski]

That would also break all existing code that uses multidimensional arrays.

[JeffBezanson]

Actually I'd like for (i,j) in product(x,y) for flattened iteration over
multiple things.

[garborg]

+1 for product

[RaulDurand]

May be I am wrong but product may not work when the second range depends on the first.
In the example below there is no way to use product because the second iteration is done in different sets of 'children':

children = Child[]
for parent in parents
    for child in parent.children
          push!(children, child)
    end
end

On the other hand, trying to make a direct translation into a comprehension we could have:

children = [ child for parent in parents for child in parent.children ]

or even, including an if clause:

children = [ child for parent in parents for child in parent.children if child.age<12 ]

When I work with finite elements, usually I have to do:

all_dofs = Dof[]
for elem in elems
    for node in elem.nodes
        for dof in node.dofs
            push!(all_dofs, dof)
        end
    end
end

A similar translation into a comprehension leads to:

all_dofs = [ dof for elem in elems for node in elem.nodes for dof in node.dofs ]

The use of multiple for seems natural in the above 1d examples and I don't think we need to associate the number of for with the number of dimensions.

IMHO, I think that the use of commas are ok for multidimensional arrays since it is similar to the use of commas for indexing (for example A[i,j] or B[i,j,k]) and the array sizes in each dimension are known a priori.