Circular array in Julia

Is the a simple way in Julia to define circular array, e.g., if I have:

x=zeros(4,4)

I would like that:

x[1,5] = x[1,1]
x[1,6] = x[1,2]

and

x[5,1] = x[1,1]
x[6,1] = x[2,1]

I would like to define a more complex grid topology so simple solution like adding the reminder operator:

x[1%4,5%4]

will not help

1 Like

Welcome to Julia’s Discourse forum!, about your question, you can define your own array type, defining the necessary interfaces (see this link). for example, a starting base can be this (supposing the circular size is the size of the data):

struct CircularArray{T,N} <: AbstractArray{T,N}
    x::AbstractArray{T,N}
end

the next step would be defining the basic operations: size, getindex and setindex!. here i have some trouble, if someone can help, it can be appreciated.

size(A::CircularArray) = size(A.x)

anyway, if this is made, it can be a nice adition to DataStructures.jl

Also, related post from discourse can help:

The question is not super-clear, but I am under the impression that @udistr may just be looking for a function that makes this array, and may be fine with a Matrix. In that case, a loop should be fine.

Thanks longemen3000,

Defining a new array type was my direction also. But I am still not sure how to implement the basic operations getindex and setindex!. This is so far what I was able to come up with:

struct CircularArray
    x
end

function (getindex::CircularArray)(i,j)

  x=getindex.x
  S=size(x);
  nx=S[1];ny=S[2];
  
  if (i>0 && i<=nx) && (j>0 && j<=ny)  
    return x[i,j]
  else     
    if i<1
      i1 = nx+i
      j1 = j
      return getindex(i1,j1)
    end
    if i>nx
      i1 = i-nx
      j1 = j     
      return getindex(i1,j1)
    end
    if j<1
      i1 = i
      j1 = ny+j
      return getindex(i1,j1)
    end
    if j>ny
      i1 = i
      j1 = j-ny
      return getindex(i1,j1)
    end
  end
end

x=reshape(collect(0:15).%4 .+1,(4,4));
y=x'

x1=CircularArray(x)
y1=CircularArray(y)

i=0;j=1;
x1(i,j),y1(i,j)

What should I do in order to be able to get the index with square brackets - x1[5,1] and how to set values, e.g., x[5,1]=1 ?

I do plan to use this for finite difference calculations but for some operations, such as box mean, it is not enough to have only the halo.

so, you need negative implementations?, lets see what can i do

There is a typo there, it should be:

i1 = nx+i

try this, the implementation is multidimentional

struct CircularArray{T,N} <: AbstractArray{T,N} #inherits from AbstractArray
    x::AbstractArray{T,N}
    function CircularArray(x::AbstractArray{T,N}) where {T,N} 
#creates the type only with a vector x
        return new{T,N}(x)
    end
end

Base.size(A::CircularArray) = size(A.x) #important: use of Base.function

Base.length(A::CircularArray)=length(A.x)

function Base.getindex(A::CircularArray, I::Vararg{Int, N}) where N # implements A[I]
    I2 = size(A)
    return Base.getindex(A.x,(mod.(I .- 1,I2) .+ 1)...) #this is the magic operation
end

Base.getindex(A::CircularArray, I) = (A[i] for i in I) #A[1:5], for example

function Base.setindex!(A,value,I::Vararg{Int, N}) where N # A[I] = value
    return Base.setindex!(A.x,value,(mod.(I .- 1,I2) .+ 1)...)
end

Base.IndexStyle(::Type{CircularArray}) = IndexCartesian() 

example code:

x=reshape(collect(0:15).%4 .+1,(4,4));
y=x'

x1=CircularArray(x)
y1=CircularArray(y)

i=0;j=1;
x1[i,j],y1[i,j]

this works in N dimensions:

#1-dimentional example
z = 1:15
z2 = CircularArray(z)
z2[16] # 1
z3 = collect(z2[14:16]) #[14,15,1]

When implementing a circular array, doesn’t it make much more sense to use 0-based indexing?

2 Likes

maybe, my toughts were to preserve the 1-based indexing of julia, and preserve the equality circular_x[i,j] == x[i,j]

1 Like

There exists an implementation in ShiftedArrays: https://github.com/piever/ShiftedArrays.jl/blob/master/src/circshiftedarray.jl

If you need something more complex but along these lines, hopefully it can serve as a starting point to write your own custom array type.

1 Like

And there is the mod1 function to avoid all this shifting indices manually:

julia> mod1(5,5)
5

julia> mod1(6,5)
1
2 Likes

Thanks again longemen3000 (and others)! This do what I want except this:

julia> x1[:,0]
ERROR: BoundsError: attempt to access 4×4 CircularArray{Int64,2} at index [Base.Slice(Base.OneTo(4)), 0]
Stacktrace:
 [1] throw_boundserror(::CircularArray{Int64,2}, ::Tuple{Base.Slice{Base.OneTo{Int64}},Int64}) at ./abstractarray.jl:484
 [2] checkbounds at ./abstractarray.jl:449 [inlined]
 [3] _getindex(::IndexCartesian, ::CircularArray{Int64,2}, ::Base.Slice{Base.OneTo{Int64}}, ::Int64) at ./multidimensional.jl:641
 [4] getindex(::CircularArray{Int64,2}, ::Function, ::Int64) at ./abstractarray.jl:927
 [5] top-level scope at none:0

x[1,0] and x[:,1] work so it is only a problem dealing with ranges outside array boundaries. Any ideas how to solve this?

1 Like

That’s just a matter of defining the appropriate checkbounds specialization. In fact, I think you can simply turn off bounds checks entirely:

Base.checkbounds(A::CircularArray, I...) = nothing
3 Likes

This is material for a small compact package!

1 Like