What is the simplest way to iterate over an array of arrays? - julia

Question

Let x::Vector{Vector{T}}. What is the best way to iterate over all the elements of each inner vector (that is, all elements of type T)? The best I can come up with is a double iteration using the single-line notation, ie:
for n in eachindex(x), m in eachindex(x[n])
x[n][m]
end
but I'm wondering if there is a single iterator, perhaps in the Iterators package, designed specifically for this purpose, e.g. for i in some_iterator(x) ; x[i] ; end.
More generally, what about iterating over the inner-most elements of any array of arrays (that is, arrays of any dimension)?

Answer 1

Your way
for n in eachindex(x), m in eachindex(x[n])
x[n][m]
end
is pretty fast. If you want best speed, use
for n in eachindex(x)
y = x[n]
for m in eachindex(y)
y[m]
end
end
which avoids dereferencing twice (the first dereference is hard to optimize out because arrays are mutable, and so getindex isn't pure). Alternatively, if you don't need m and n, you could just use
for y in x, for z in y
z
end
which is also fast.
Note that column-major storage is irrelevant, since all arrays here are one-dimensional.
To answer your general question:
If the number of dimensions is a compile-time constant, see Base.Cartesian
If the number of dimensions is not a compile-time constant, use recursion
And finally, as Dan Getz mentioned in a comment:
using Iterators
for z in chain(x...)
z
end
also works. This however has a bit of a performance penalty.

Answer 2

I'm wondering if there is a single iterator, perhaps in the Iterators package, designed specifically for this purpose, e.g. for i in some_iterator(x) ; x[i] ; end
Today (in Julia 1.x versions), Iterators.flatten is exactly this.
help?> Iterators.flatten
flatten(iter)
Given an iterator that yields iterators, return an iterator that
yields the elements of those iterators. Put differently, the
elements of the argument iterator are concatenated.
julia> x = [1:5, [π, ℯ, 42], 'a':'e']
3-element Vector{AbstractVector}:
1:5
[3.141592653589793, 2.718281828459045, 42.0]
'a':1:'e'
julia> for el in Iterators.flatten(x)
print(el, " ")
end
1 2 3 4 5 3.141592653589793 2.718281828459045 42.0 a b c d e
julia>