ShiftedArrays

Implementation of shifted arrays.

Shifted Arrays

A ShiftedArray is a lazy view of an Array, shifted on some or all of his indexing dimensions by some constant values.

julia> v = reshape(1:16, 4, 4)
4×4 reshape(::UnitRange{Int64}, 4, 4) with eltype Int64:
 1  5   9  13
 2  6  10  14
 3  7  11  15
 4  8  12  16

julia> s = ShiftedArray(v, (2, 0))
4×4 ShiftedArray{Int64, Missing, 2, Base.ReshapedArray{Int64, 2, UnitRange{Int64}, Tuple{}}}:
  missing   missing    missing    missing
  missing   missing    missing    missing
 1         5          9         13
 2         6         10         14 

The parent Array as well as the amount of shifting can be recovered with parent and shifts respectively.

julia> parent(s)
4×4 reshape(::UnitRange{Int64}, 4, 4) with eltype Int64:
 1  5   9  13
 2  6  10  14
 3  7  11  15
 4  8  12  16

julia> shifts(s)
(2, 0)

shifts returns a Tuple, where the n-th element corresponds to the shift on the n-th dimension of the parent Array.

Use copy to collect the shifted data into an Array:

julia> copy(s)
4×4 Matrix{Union{Missing, Int64}}:
  missing   missing    missing    missing
  missing   missing    missing    missing
 1         5          9         13
 2         6         10         14   

If you pass an integer, it will shift in the first dimension:

julia> ShiftedArray(v, 1)
4×4 ShiftedArray{Int64, Missing, 2, Base.ReshapedArray{Int64, 2, UnitRange{Int64}, Tuple{}}}:
  missing   missing    missing    missing
 1         5          9         13
 2         6         10         14
 3         7         11         15

A custom default value (other than missing) can be provided with the default keyword:

julia> ShiftedArray([1.2, 3.1, 4.5], 1, default = NaN)
3-element ShiftedVector{Float64, Float64, Vector{Float64}}:
 NaN
   1.2
   3.1

Out of bound indexes

Accessing indexes outside the ShiftedArray give a BoundsError, even if the shifted index would have been valid in the parent array.

julia> ShiftedArray([1, 2, 3], 1)[4]
ERROR: BoundsError: attempt to access 3-element ShiftedVector{Int64, Missing, Vector{Int64}} at index [4]

Shifting the data

Using the ShiftedArray type, this package provides two operations for lazily shifting vectors: lag and lead.

julia> v = [1, 3, 5, 4];

julia> ShiftedArrays.lag(v)
4-element ShiftedVector{Int64, Missing, Vector{Int64}}:
  missing
 1
 3
 5       

julia> v .- ShiftedArrays.lag(v) # compute difference from previous element without unnecessary allocations
4-element Vector{Union{Missing, Int64}}:
   missing
  2
  2
 -1       

julia> s = ShiftedArrays.lag(v, 2) # shift by more than one element
4-element ShiftedVector{Int64, Missing, Vector{Int64}}:
  missing
  missing
 1
 3

lead is the analogous of lag but shifts in the opposite direction:

julia> v = [1, 3, 5, 4];

julia> ShiftedArrays.lead(v)
4-element ShiftedVector{Int64, Missing, Vector{Int64}}:
 3
 5
 4
  missing

Shifting the data circularly

Julia Base provides a function circshift to shift the data circularly. However this function creates a copy of the vector, which may be unnecessary if the rotated vector is to be used only once. This package provides the CircShiftedArray type, which is a lazy view of an array shifted on some or all of his indexing dimensions by some constant values.

Our implementation of circshift relies on them to avoid copying:

julia> w = reshape(1:16, 4, 4);

julia> s = ShiftedArrays.circshift(w, (1, -1))
4×4 CircShiftedArray{Int64, 2, Base.ReshapedArray{Int64, 2, UnitRange{Int64}, Tuple{}}}:
 8  12  16  4
 5   9  13  1
 6  10  14  2
 7  11  15  3

As usual, you can copy the result to have a normal Array:

julia> copy(s)
4×4 Matrix{Int64}:
 8  12  16  4
 5   9  13  1
 6  10  14  2
 7  11  15  3