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Julia and arrays with custom indices

Julia is a modern language designed for technical computing. In the spirit of other scientific languages such as Fortran, MATLAB/Octave, Mathematica, and R, Julia uses 1-based indexing for arrays. Meaning that the first element of an one-dimensional array a is accessed with a[1]. This is in contrast to popular languages such as C and Python which use 0-based indexing and that though they came to be used in sciences they weren’t specifically designed for them.

But like Fortran, Julia though it defaults to 1-based, it allows you to specify arbitrary indices for the arrays. The documentation is very good, showing how to generalize the code, bound check and do loops but is more oriented to developers. Meaning even if they’re are good techniques it is not something someone that wants to implement a simple algorithm will find straightforward to apply.

For this the OffsetArrays.jl package may be used. This package can be utilized to provide arbitrary indices in similar vein to Fortan. Specifically it exports the following OffsetArray function.

help?> OffsetArray
  OffsetArray(A, indices...)

That function returns an AbstractArray sharing element type and size with supplied array A but uses axes inferred from the supplied indices argument.

Let’s define an one-dimensional array a.

julia> a = collect(1:5)
5-element Array{Int64,1}:
 1
 2
 3
 4
 5

Elements in a loop can be accessed counting from 1 to length(a).

julia> i=1;

julia> a[i]
1

In order to change the loop from 0 to length(a)-1, the following can be run.

julia> using OffsetArrays

julia> a = OffsetArray(a, 0:(length(a) - 1))
5-element OffsetArray(::Array{Int64,1}, 0:4) with eltype Int64 with indices 0:4:
 1
 2
 3
 4
 5

Then

julia> i=0;

julia> a[i]
1

For simpler usage the following function can be defined

function zero_based(a)
    return OffsetArray(a, 0:(length(a) - 1))
end

Then

julia> a = collect(1:5);

julia> a = zero_based(a)
5-element OffsetArray(::Array{Int64,1}, 0:4) with eltype Int64 with indices 0:4:
 1
 2
 3
 4
 5

Another usage is when we wish to access elements of a region referred from an array, using the indices corresponding to the originating array. For an example, let’s define a two-dimensional array A.

julia> A = reshape(1:36, 6, 6)
6×6 reshape(::UnitRange{Int64}, 6, 6) with eltype Int64:
 1   7  13  19  25  31
 2   8  14  20  26  32
 3   9  15  21  27  33
 4  10  16  22  28  34
 5  11  17  23  29  35
 6  12  18  24  30  36

A region may be referred as follows.

julia> B = A[2:5, 2:5]
4×4 Array{Int64,2}:
  8  14  20  26
  9  15  21  27
 10  16  22  28
 11  17  23  29

Now as things are the elements of A and B do not correspond.

julia> A[2, 2]
8

julia> B[1, 1]
8

To make indexing consistent the following can be run.

julia> B = OffsetArray(A[2:5, 2:5], 2:5, 2:5)
4×4 OffsetArray(::Array{Int64,2}, 2:5, 2:5) with eltype Int64 with indices 2:5×2:5:
  8  14  20  26
  9  15  21  27
 10  16  22  28
 11  17  23  29

Then

julia> A[2, 2]
8

julia> B[2, 2]
8

For simpler usage the following function can be defined

function refer_region(A, x, y)
    return OffsetArray(A[x, y], x, y)
end

Then

julia> A = reshape(1:36, 6, 6);

julia> B = refer_region(A, 2:5, 2:5)
4×4 OffsetArray(::Array{Int64,2}, 2:5, 2:5) with eltype Int64 with indices 2:5×2:5:
  8  14  20  26
  9  15  21  27
 10  16  22  28
 11  17  23  29

Those are some trivial examples to showcase arbitrary indices. Since Julia defaults to 1 some codes and packages may see this as absolute. Meaning that custom indices may create issues and trigger errors, even in base Julia. It should be noted that the last example was taken from Holy’s post on Julia blog which has about similar theme to this post but is more extended and detailed.