[dlfivefifty]

Adds FillArrays.OffDiagonal, a matrix whose only nonzero entries lie on a single diagonal:

julia> FillArrays.OffDiagonal([1, 2, 3], 1)
4×4 FillArrays.OffDiagonal{Int64, Vector{Int64}, Tuple{Base.OneTo{Int64}, Base.OneTo{Int64}}}:
 ⋅  1  ⋅  ⋅
 ⋅  ⋅  2  ⋅
 ⋅  ⋅  ⋅  3
 ⋅  ⋅  ⋅  ⋅

OffDiagonal(band, k, axes) stores band on the k-th diagonal, using the same convention as diag/diagind (k > 0 is above the diagonal). length(band) must match the length of that diagonal, and may be zero if the diagonal lies outside the matrix. OffDiagonal(band, k) builds the square length(band) + abs(k) matrix.

Slicing

Indexing these types by unit ranges or : now returns an OffDiagonal instead of a dense Matrix:

• Diagonal{<:Number,<:AbstractFillVector} (including square Eye)
• any RectDiagonal (including rectangular Eye)
• OffDiagonal itself

A slice of any of these matrices has nonzeros on at most one diagonal, so the result needs only a new band offset and a slice of the band. Lazy bands stay lazy, and the slice doesn't allocate:

julia> Eye(5)[2:4, 1:3] === FillArrays.OffDiagonal(Ones(2), 1, 3, 3)
true

julia> @allocated Eye(5)[2:4, 1:3]
0

What still takes the existing path:

• Diagonals not backed by a fill, such as Diagonal([1, 2, 3])[1:2, 1:2], still return a Matrix.
• Indices whose result would have offset or infinite axes fall back to the generic getindex.
• Diagonal fills with non-Number eltypes (block diagonals) are left alone, because OffDiagonal fills off-band entries with zero(T).

OffDiagonal also gets setindex! (on the band only), diag, ⋅ printing for zeros, and hashing alongside RectDiagonal. Like RectDiagonal, it isn't exported.

The version is bumped to 1.18.0, since these slices now return a different type.

Tests

The new testset checks every contiguous sub-range of a set of Eye, Diagonal fill, RectDiagonal and OffDiagonal matrices against dense slicing: square and rectangular, Vector and Fill bands, sub- and superdiagonals, and empty bands.

🤖 Generated with Claude Code

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[dlfivefifty]

The motivation for this is so that eg Eye(n)[1:n,2:n] will return a sparse type. But actually I'm planning to use this in ArrayLayouts.jl for all Diagonal{T, <:LayoutArray}.

The only potential downside is if someone expects slicing to make a mutable array. But we already break that assumption for Fill etc. so I think it's OK. And my view if it doesn't break any unit tests / integration tests then it doesn't count as breaking.