PaddedViews
Summary
PaddedViews provides a simple wrapper type, PaddedView, to add
"virtual" padding to any array without copying data. Edge values not
specified by the array are assigned a fillvalue. Multiple arrays
may be "promoted" to have common indices using the paddedviews
function.
PaddedView arrays are read-only, meaning that you cannot assign
values to them. The original array may be extracted using A = parent(P), where P is a PaddedView.
Examples
For padding a single array:
julia> a = collect(reshape(1:9, 3, 3))
3×3 Array{Int64,2}:
1 4 7
2 5 8
3 6 9
julia> PaddedView(-1, a, (4, 5))
4×5 PaddedView(-1, ::Array{Int64,2}, (Base.OneTo(4), Base.OneTo(5))) with eltype Int64:
1 4 7 -1 -1
2 5 8 -1 -1
3 6 9 -1 -1
-1 -1 -1 -1 -1
julia> PaddedView(-1, a, (1:5,1:5), (2:4,2:4))
5×5 PaddedView(-1, OffsetArray(::Array{Int64,2}, 2:4, 2:4), (1:5, 1:5)) with eltype Int64 with indices 1:5×1:5:
-1 -1 -1 -1 -1
-1 1 4 7 -1
-1 2 5 8 -1
-1 3 6 9 -1
-1 -1 -1 -1 -1
julia> PaddedView(-1, a, (0:4, 0:4))
5×5 PaddedView(-1, ::Array{Int64,2}, (0:4, 0:4)) with eltype Int64 with indices 0:4×0:4:
-1 -1 -1 -1 -1
-1 1 4 7 -1
-1 2 5 8 -1
-1 3 6 9 -1
-1 -1 -1 -1 -1
julia> PaddedView(-1, a, (5,5), (2,2))
5×5 PaddedView(-1, OffsetArray(::Array{Int64,2}, 2:4, 2:4), (Base.OneTo(5), Base.OneTo(5))) with eltype Int64:
-1 -1 -1 -1 -1
-1 1 4 7 -1
-1 2 5 8 -1
-1 3 6 9 -1
-1 -1 -1 -1 -1For padding multiple arrays to have common indices:
julia> a1 = reshape([1, 2, 3], 3, 1)
3×1 Array{Int64,2}:
1
2
3
julia> a2 = [4 5 6]
1×3 Array{Int64,2}:
4 5 6
julia> a1p, a2p = paddedviews(-1, a1, a2);
julia> a1p
3×3 PaddedView(-1, ::Array{Int64,2}, (Base.OneTo(3), Base.OneTo(3))) with eltype Int64:
1 -1 -1
2 -1 -1
3 -1 -1
julia> a2p
3×3 PaddedView(-1, ::Array{Int64,2}, (Base.OneTo(3), Base.OneTo(3))) with eltype Int64:
4 5 6
-1 -1 -1
-1 -1 -1If you want original arrays in the center of padded results:
julia> a1 = reshape([1, 2, 3], 3, 1)
3×1 Array{Int64,2}:
1
2
3
julia> a2 = [4 5 6]
1×3 Array{Int64,2}:
4 5 6
julia> a1p, a2p = sym_paddedviews(-1, a1, a2);
julia> a1p
3×3 PaddedView(-1, ::Array{Int64,2}, (1:3, 0:2)) with eltype Int64 with indices 1:3×0:2:
-1 1 -1
-1 2 -1
-1 3 -1
julia> a2p
3×3 PaddedView(-1, ::Array{Int64,2}, (0:2, 1:3)) with eltype Int64 with indices 0:2×1:3:
-1 -1 -1
4 5 6
-1 -1 -1We can use dims keyword to specify the direction of padding for the output arrays as shown above. They can be integers or tuple of integers.
julia> a1p, a2p = paddedviews(-1, a1, a2; dims=1);
julia> a1p
3×1 PaddedView(-1, ::Matrix{Int64}, (Base.OneTo(3), Base.OneTo(1))) with eltype Int64:
1
2
3
julia> a2p
3×3 PaddedView(-1, ::Matrix{Int64}, (Base.OneTo(3), Base.OneTo(3))) with eltype Int64:
4 5 6
-1 -1 -1
-1 -1 -1
julia> a1p, a2p = sym_paddedviews(-1, a1, a2; dims=2);
julia> a1p
3×3 PaddedView(-1, ::Matrix{Int64}, (1:3, 0:2)) with eltype Int64 with indices 1:3×0:2:
-1 1 -1
-1 2 -1
-1 3 -1
julia> a2p
1×3 PaddedView(-1, ::Matrix{Int64}, (1:1, 1:3)) with eltype Int64 with indices 1:1×1:3:
4 5 6