PeriodicArrays.jl

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PeriodicArrays.jl adds the PeriodicArray type which can be backed by any AbstractArray. The idea of this package is based on CircularArrays.jl and extends its functionality to support user-defined translation rules for periodic indexing. A PeriodicArray{T,N,A,F} is an AbstractArray{T,N} backed by a data array of type A<:AbstractArray{T,N} and a map f of type F. The map defines how data in out-of-bounds indices is translated to valid indices in the data array.

f can be any callable object (e.g. a function or a struct), which defines

f(x, shift::Vararg{Int,N})

where x is an element of the array and shift encodes the unit cell, in which we index. f has to satisfy the following properties, which are not checked at construction time:

• The output type of f has to be the same as the element type of the data array.
• f is invertible with inverse f(x, -shift...), i.e. it satisfies f(f(x, shift...), -shift...) == x.

If f is not provided, the identity map is used and the PeriodicArray behaves like a CircularArray.

This package is compatible with OffsetArrays.jl.

Installation

The package is registered in the Julia general registry. It can be installed trough the package manager with the following command:

pkg> add PeriodicArrays

Code Samples

julia> using PeriodicArrays
julia> a = PeriodicVector([1,2,3])
julia> a[0:4]
5-element PeriodicVector(::Vector{Int64}):
 3
 1
 2
 3
 1
julia> f(x, shift...) = x + 10 * sum(shift)
julia> a2 = PeriodicArray([1,2,3], f);
julia> a2[0:4]
5-element PeriodicVector(::Vector{Int64}):
 -7
  1
  2
  3
 11
julia> struct MyTranslator end;
julia> (f::MyTranslator)(x, shift) = x - shift;
julia> a3 = PeriodicArray([1,2,3], MyTranslator());
julia> a3[0:4]
5-element PeriodicVector(::Vector{Int64}):
 4
 1
 2
 3
 0
julia> using OffsetArrays
julia> data = reshape(1:9, 3, 3);
julia> i = OffsetArray(1:5, -2:2);
julia> a4 = PeriodicMatrix(data, f);
julia> a4[i,i]
5×5 PeriodicArray(OffsetArray(::Matrix{Int64}, -2:2, -2:2)) with indices -2:2×-2:2:
  1   4   7  11  14
  2   5   8  12  15
  3   6   9  13  16
 11  14  17  21  24
 12  15  18  22  25

License

PeriodicArrays.jl is licensed under the MIT License. By using or interacting with this software in any way, you agree to the license of this software.