Avoid memory allocation when indexing an array in Julia

Question

UPDATE: Note that the relevant function in Julia v1+ is view

Question: I would like to index into an array without triggering memory allocation, especially when passing the indexed elements into a function. From reading the Julia docs, I suspect the answer revolves around using the sub function, but can't quite see how...

Working Example: I build a large vector of Float64 (x) and then an index to every observation in x.

N = 10000000
x = randn(N)
inds = [1:N]

Now I time the mean function over x and x[inds] (I run mean(randn(2)) first to avoid any compiler irregularities in the timing):

@time mean(x)
@time mean(x[inds])

It's an identical calculation, but as expected the results of the timings are:

elapsed time: 0.007029772 seconds (96 bytes allocated)
elapsed time: 0.067880112 seconds (80000208 bytes allocated, 35.38% gc time)

So, is there a way around the memory allocation problem for arbitrary choices of inds (and arbitrary choice of array and function)?

Answer 1

Just use xs = sub(x, 1:N). Note that this is different from x = sub(x, [1:N]); on julia 0.3 the latter will fail, and on julia 0.4-pre the latter will be considerably slower than the former. On julia 0.4-pre, sub(x, 1:N) is just as fast as view:

julia> N = 10000000;

julia> x = randn(N);

julia> xs = sub(x, 1:N);

julia> using ArrayViews

julia> xv = view(x, 1:N);

julia> mean(x)
-0.0002491126429772525

julia> mean(xs)
-0.0002491126429772525

julia> mean(xv)
-0.0002491126429772525

julia> @time mean(x);
elapsed time: 0.015345806 seconds (27 kB allocated)

julia> @time mean(xs);
elapsed time: 0.013815785 seconds (96 bytes allocated)

julia> @time mean(xv);
elapsed time: 0.015871052 seconds (96 bytes allocated)

There are several reasons why sub(x, inds) is slower than sub(x, 1:N):

• Each access xs[i] corresponds to x[inds[i]]; we have to look up two memory locations rather than one
• If inds is not in order, you will get poor cache behavior in accessing the elements of x
• It destroys the ability to use SIMD vectorization

In this case, the latter is probably the most important effect. This is not a Julia limitation; the same thing would happen were you to write the equivalent code in C, Fortran, or assembly.

Note that it's still faster to say sum(sub(x, inds)) than sum(x[inds]), (until the latter becomes the former, which it should by the time julia 0.4 is officially out). But if you have to do many operations with xs = sub(x, inds), in some circumstances it will be worth your while to make a copy, even though it allocates memory, just so you can take advantage of the optimizations possible when values are stored in contiguous memory.