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Finite sections of JacobiTriangle Jacobi matrices are ApplyArrays instead of BandedBlockBandedMatrices #216
Description
I don't think this used to be the case.
julia> jacobimatrix(Val(1), RectPolynomial(ChebyshevT(), ChebyshevT()))[Block.(1:5), Block.(1:5)]
5×5-blocked 15×15 BandedBlockBandedMatrix{Float64} with block-bandwidths (1, 1) and sub-block-bandwidths block-bandwidths (0, 0) with data 3×5-blocked 3×15 BlockedMatrix{Float64}:
0.0 │ 0.5 ⋅ │ ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅
─────┼────────────┼─────────────────┼──────────────────────┼─────────────────────────
1.0 │ 0.0 ⋅ │ 0.5 ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ │ ⋅ 0.0 │ ⋅ 0.5 ⋅ │ ⋅ ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅
─────┼────────────┼─────────────────┼──────────────────────┼─────────────────────────
⋅ │ 0.5 ⋅ │ 0.0 ⋅ ⋅ │ 0.5 ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ │ ⋅ 1.0 │ ⋅ 0.0 ⋅ │ ⋅ 0.5 ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ │ ⋅ ⋅ │ ⋅ ⋅ 0.0 │ ⋅ ⋅ 0.5 ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅
─────┼────────────┼─────────────────┼──────────────────────┼─────────────────────────
⋅ │ ⋅ ⋅ │ 0.5 ⋅ ⋅ │ 0.0 ⋅ ⋅ ⋅ │ 0.5 ⋅ ⋅ ⋅ ⋅
⋅ │ ⋅ ⋅ │ ⋅ 0.5 ⋅ │ ⋅ 0.0 ⋅ ⋅ │ ⋅ 0.5 ⋅ ⋅ ⋅
⋅ │ ⋅ ⋅ │ ⋅ ⋅ 1.0 │ ⋅ ⋅ 0.0 ⋅ │ ⋅ ⋅ 0.5 ⋅ ⋅
⋅ │ ⋅ ⋅ │ ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ 0.0 │ ⋅ ⋅ ⋅ 0.5 ⋅
─────┼────────────┼─────────────────┼──────────────────────┼─────────────────────────
⋅ │ ⋅ ⋅ │ ⋅ ⋅ ⋅ │ 0.5 ⋅ ⋅ ⋅ │ 0.0 ⋅ ⋅ ⋅ ⋅
⋅ │ ⋅ ⋅ │ ⋅ ⋅ ⋅ │ ⋅ 0.5 ⋅ ⋅ │ ⋅ 0.0 ⋅ ⋅ ⋅
⋅ │ ⋅ ⋅ │ ⋅ ⋅ ⋅ │ ⋅ ⋅ 0.5 ⋅ │ ⋅ ⋅ 0.0 ⋅ ⋅
⋅ │ ⋅ ⋅ │ ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ 1.0 │ ⋅ ⋅ ⋅ 0.0 ⋅
⋅ │ ⋅ ⋅ │ ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ 0.0
julia> typeof(ans)
BlockBandedMatrices.BandedBlockBandedMatrix{Float64, BlockedMatrix{Float64, Matrix{Float64}, Tuple{BlockedOneTo{Int64, StepRangeLen{Int64, Int64, Int64, Int64}}, BlockedOneTo{Int64, Vector{Int64}}}}, BlockedOneTo{Int64, Vector{Int64}}}
julia> jacobimatrix(Val(1), JacobiTriangle())[Block.(1:5), Block.(1:5)]
(5×5-blocked 15×15 BandedBlockBandedMatrix{Float64} with block-bandwidths (1, 0) and sub-block-bandwidths block-bandwidths (0, 0) with data 2×5-blocked 2×15 BlockVcat{Float64}) * (5×5-blocked 15×15 BandedBlockBandedMatrix{Float64} with block-bandwidths (0, 1) and sub-block-bandwidths block-bandwidths (0, 0) with data 2×5-blocked 2×15 BlockVcat{Float64}) with indices BlockedOneTo([1, 3, 6, 10, 15])×BlockedOneTo([1, 3, 6, 10, 15]):
0.333333 │ 0.166667 ⋅ │ ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅
──────────┼─────────────────┼────────────────────────────────┼──────────────────────────────────────────┼────────────────────────────────────────────────────
0.333333 │ 0.466667 ⋅ │ 0.2 ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ │ ⋅ 0.2 │ ⋅ 0.133333 ⋅ │ ⋅ ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅
──────────┼─────────────────┼────────────────────────────────┼──────────────────────────────────────────┼────────────────────────────────────────────────────
⋅ │ 0.3 ⋅ │ 0.485714 ⋅ ⋅ │ 0.214286 ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ │ ⋅ 0.2 │ ⋅ 0.371429 ⋅ │ ⋅ 0.178571 ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ │ ⋅ ⋅ │ ⋅ ⋅ 0.142857 │ ⋅ ⋅ 0.107143 ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅
──────────┼─────────────────┼────────────────────────────────┼──────────────────────────────────────────┼────────────────────────────────────────────────────
⋅ │ ⋅ ⋅ │ 0.285714 ⋅ ⋅ │ 0.492063 ⋅ ⋅ ⋅ │ 0.222222 ⋅ ⋅ ⋅ ⋅
⋅ │ ⋅ ⋅ │ ⋅ 0.238095 ⋅ │ ⋅ 0.428571 ⋅ ⋅ │ ⋅ 0.2 ⋅ ⋅ ⋅
⋅ │ ⋅ ⋅ │ ⋅ ⋅ 0.142857 │ ⋅ ⋅ 0.301587 ⋅ │ ⋅ ⋅ 0.155556 ⋅ ⋅
⋅ │ ⋅ ⋅ │ ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ 0.111111 │ ⋅ ⋅ ⋅ 0.0888889 ⋅
──────────┼─────────────────┼────────────────────────────────┼──────────────────────────────────────────┼────────────────────────────────────────────────────
⋅ │ ⋅ ⋅ │ ⋅ ⋅ ⋅ │ 0.277778 ⋅ ⋅ ⋅ │ 0.494949 ⋅ ⋅ ⋅ ⋅
⋅ │ ⋅ ⋅ │ ⋅ ⋅ ⋅ │ ⋅ 0.25 ⋅ ⋅ │ ⋅ 0.454545 ⋅ ⋅ ⋅
⋅ │ ⋅ ⋅ │ ⋅ ⋅ ⋅ │ ⋅ ⋅ 0.194444 ⋅ │ ⋅ ⋅ 0.373737 ⋅ ⋅
⋅ │ ⋅ ⋅ │ ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ 0.111111 │ ⋅ ⋅ ⋅ 0.252525 ⋅
⋅ │ ⋅ ⋅ │ ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ │ ⋅ ⋅ ⋅ ⋅ 0.0909091
julia> typeof(ans)
LazyArrays.ApplyArray{Float64, 2, typeof(*), Tuple{BlockBandedMatrices.BandedBlockBandedMatrix{Float64, LazyBandedMatrices.BlockVcat{Float64, 2, Tuple{Adjoint{Float64, BlockVector{Float64, Vector{Vector{Float64}}, Tuple{BlockedOneTo{Int64, Vector{Int64}}}}}, Adjoint{Float64, BlockVector{Float64, Vector{Vector{Float64}}, Tuple{BlockedOneTo{Int64, Vector{Int64}}}}}}, Tuple{BlockedOneTo{Int64, StaticArraysCore.SVector{2, Int64}}, BlockedOneTo{Int64, Vector{Int64}}}}, BlockedOneTo{Int64, Vector{Int64}}}, BlockBandedMatrices.BandedBlockBandedMatrix{Float64, LazyBandedMatrices.BlockVcat{Float64, 2, Tuple{Adjoint{Float64, BlockVector{Float64, Vector{Vector{Float64}}, Tuple{BlockedOneTo{Int64, Vector{Int64}}}}}, Adjoint{Float64, BlockVector{Float64, Vector{Vector{Float64}}, Tuple{BlockedOneTo{Int64, Vector{Int64}}}}}}, Tuple{BlockedOneTo{Int64, StaticArraysCore.SVector{2, Int64}}, BlockedOneTo{Int64, Vector{Int64}}}}, BlockedOneTo{Int64, Vector{Int64}}}}}
Activity
dlfivefifty commentedon Mar 26, 2026
Does this matter in practice? You can always convert explicitly:
dlfivefifty commentedon Mar 26, 2026
There is a fundamental question that there's ambiguity about when something should be left lazy versus materialised. The change probably came about to support something infinite dimensional, and as no tests failed it was merged.
Without a firm guideline on what the right choice is I'm inclined to not worry about this, unless there's a very argument why it matters.