Transform nested array into new dimension

Question

Given an array as follows:

A = Array{Array{Int}}(2,2)
A[1,1] = [1,2]
A[1,2] = [3,4]
A[2,1] = [5,6]
A[2,2] = [7,8]

We then have that A is a 2x2 array with elements of type Array{Int}:

2×2 Array{Array{Int64,N} where N,2}:
 [1, 2]  [3, 4]
 [5, 6]  [7, 8]

It is possible to access the entries with e.g. A[1,2] but A[1,2,2] would not work since the third dimension is not present in A. However, A[1,2][2] works, since A[1,2] returns an array of length 2.

The question is then, what is a nice way to convert A into a 3-dimensional array, B, so that B[i,j,k] refers the the i,j-th array and the k-th element in that array. E.g. B[2,1,2] = 6.

There is a straightforward way to do this using 3 nested loops and reconstructing the array, element-by-element, but I'm hoping there is a nicer construction. (Some application of cat perhaps?)

cat(3,first.(A),last.(A)) also gives the same matrix. If more than two elements in internal vectors, getindex can be used to generalize this construction. — Dan Getz
– Dan Getz, Commented Nov 10, 2017 at 13:58
I figured out one way: B = permutedims(reshape(collect(Iterators.flatten(A)), (2,2,2)), [3,2,1]), but it is very badly readable and I'd rather use the generators from @durand's answer below. To generalise your answer: cat(3, map(idx -> getindex.(A, idx),(1:2))...) may be alright (for suitable ranges). — Calavoow
– Calavoow, Commented Nov 10, 2017 at 14:43
The expressions in your comment can also be written: permutedims(reshape(vcat(A...),2,2,2),[2,3,1]) and cat(3,(getindex.(A,i) for i=1:2)...) — Dan Getz
– Dan Getz, Commented Nov 10, 2017 at 14:56

Raul Durand · Accepted Answer · 2017-11-09 22:52:19Z

2

You can construct a 3-d array from A using an array comprehension

julia> B = [ A[i,j][k] for i=1:2, j=:1:2, k=1:2 ]
2×2×2 Array{Int64,3}:
[:, :, 1] =
 1  3
 5  7

[:, :, 2] =
 2  4
 6  8

julia> B[2,1,2]
6

However a more general solution would be to overload the getindex function for arrays with the same type of A. This is more efficient since there is no need to copy the original data.

julia> import Base.getindex

julia> getindex(A::Array{Array{Int}}, i::Int, j::Int, k::Int) = A[i,j][k]
getindex (generic function with 179 methods)

julia> A[2,1,2]
6

answered Nov 9, 2017 at 22:52

Raul Durand

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Comments

Calavoow · Accepted Answer · 2017-11-20 19:30:01Z

0

With thanks to Dan Getz's comments, I think the following works well and is succinct:

cat(3,(getindex.(A,i) for i=1:2)...)

where 2 is the length of the nested array. It would also work for higher dimensions.

answered Nov 20, 2017 at 19:30

Calavoow

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Comments

carstenbauer · Accepted Answer · 2017-11-20 20:22:00Z

0

permutedims(reshape(collect(Base.Iterators.flatten(A)), (2,2,2)), (2,3,1))

also does the job and appears to be faster than the accepted cat() answer for me.

EDIT: I'm sorry, I just saw that this has already been suggested in the comments.

answered Nov 20, 2017 at 20:22

carstenbauer

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