Loops with arrays of arbitrary dimensions

General Usage
,
1

Assume that I have a 2D array A and I want to do something like this

N1, N2 = 4, 3
A = ones((N1, N2))

x = zeros(N1)
for i2=1:N2
    for i1=1:N1
        x[i1] = 2 * A[i1, i2]
    end
end

x = zeros(N2)
for i1=1:N1
    for i2=1:N2
        x[i2] = 2 * A[i1, i2]
    end
end

Then, in case of 3D array A I will need to add one extra loop:

N1, N2, N3 = 4, 3, 2
A = ones((N1, N2, N3))

x = zeros(N1)
for i3=1:N3
for i2=1:N2
    for i1=1:N1
        x[i1] = 2 * A[i1, i2, i3]
    end
end
end

# etc.

Now let’s assume I have an n-dimensional array A, and I want to specify some axis ax along which I want to multiply A by 2 and put the result to x (similarly to the above examples). The corresponding pseudo code can look like

ax = m

A = zeros((N1, N2, ..., Nn))

x = zeros(Nm)

for in=1:Nn
for i(n-1)=1:N(n-1)
...
for i(m+1)=1:N(m+1)
for i(m-1)=1:N(m-1)
...
for i2=1:N2
for i1=1:N1
    for im=1:Nm
        x[im] = 2 * A[i1, i2, ..., i(m-1), im, i(m+1), ..., i(n-1), in]
    end
end
end
...
end
end
...
end
end

However, I want a generic code which will not depend on the number of A dimensions, i.e. some function foo(x, A, ax) which will do what I want independently of the size of A. How I should write such kind of code with loops for arbitrary dimension of A?
So far I found only this old blog post which proposes to use macros. Did something changed since then? Can the corresponding loops be written with ndims and axes functions without macro?

2

You are looking for CartisianIndices

julia> x2 = rand(2, 2);

julia> x3 = rand(2, 2, 2);

julia> for c in CartesianIndices(x2)
           @show x2[c]
       end
x2[c] = 0.4108577974629497
x2[c] = 0.4591618516787277
x2[c] = 0.22742754395597542
x2[c] = 0.9850643176704423

julia> for c in CartesianIndices(x3)
           @show x3[c]
       end
x3[c] = 0.2229783161443213
x3[c] = 0.4984591608388653
x3[c] = 0.4418623143086191
x3[c] = 0.6718510628390104
x3[c] = 0.21610541455088628
x3[c] = 0.574532213871789
x3[c] = 0.02381508624762918
x3[c] = 0.9172113813322624
3

There is also @nloops [1]

[1] Base.Cartesian · The Julia Language

4

Can you please give me an example how I can write, let say, the following loop in terms of CartesianIndices:

N1, N2 = 4, 3
A = ones((N1, N2))

x = zeros(N1)
for i2=1:N2
    for i1=1:N1
        x[i1] = 2 * A[i1, i2]
    end
end

CartesianIndices(A) and CartesianIndices(x) have different dimensions.

5

I think this might be an XY problem. In the example above, you are overwriting x many times. Do you mean to have a += intead of an =?

6

Assuming this is what you want to do, you would write it like this:

for I in CartesianIndices(A)
    i1 = I[1]
    x[i1] = 2 * A[I]
end
4 Likes
7

Its just a fake example which came to my mind. It can be either of them.

8

Then @jipolanco 's solution above is what you want.

9

Thank you. Seems like what I need.
Just a small question. Why do I need to take Tuple of I? It seems to work with just I[1].

10

Oops, you’re totally right about that! I wasn’t sure that it worked.

11

Thank you all guys for the help.