julia

86231ce5 - LinearAlgebra: round-trippable 2-argument show for `Tridiagonal`/`SymTridiagonal` (#55415)

LinearAlgebra: round-trippable 2-argument show for `Tridiagonal`/`SymTridiagonal` (#55415) This makes the displayed form of a `Tridiaognal` and a `SymTridiagonal` valid constructors. ```julia julia> T = Tridiagonal(1:3, 1:4, 1:3) 4×4 Tridiagonal{Int64, UnitRange{Int64}}: 1 1 ⋅ ⋅ 1 2 2 ⋅ ⋅ 2 3 3 ⋅ ⋅ 3 4 julia> show(T) Tridiagonal(1:3, 1:4, 1:3) julia> S = SymTridiagonal(1:4, 1:3) 4×4 SymTridiagonal{Int64, UnitRange{Int64}}: 1 1 ⋅ ⋅ 1 2 2 ⋅ ⋅ 2 3 3 ⋅ ⋅ 3 4 julia> show(S) SymTridiagonal(1:4, 1:3) ``` Displaying the bands has several advantages: firstly, it's briefer than printing the full array, and secondly, it displays the special structure in the bands, if any. E.g.: ```julia julia> T = Tridiagonal(spzeros(3), spzeros(4), spzeros(3)); julia> show(T) Tridiagonal(sparsevec(Int64[], Float64[], 3), sparsevec(Int64[], Float64[], 4), sparsevec(Int64[], Float64[], 3)) ``` It's clear from the displayed form that `T` has sparse bands. A special handling for `SymTridiagonal` matrices is necessary, as the diagonal band is symmetrized. This means: ```julia julia> using StaticArrays julia> m = SMatrix{2,2}(1:4); julia> S = SymTridiagonal(fill(m,3), fill(m,2)) 3×3 SymTridiagonal{SMatrix{2, 2, Int64, 4}, Vector{SMatrix{2, 2, Int64, 4}}}: [1 3; 3 4] [1 3; 2 4] ⋅ [1 2; 3 4] [1 3; 3 4] [1 3; 2 4] ⋅ [1 2; 3 4] [1 3; 3 4] julia> show(S) SymTridiagonal(SMatrix{2, 2, Int64, 4}[[1 3; 3 4], [1 3; 3 4], [1 3; 3 4]], SMatrix{2, 2, Int64, 4}[[1 3; 2 4], [1 3; 2 4]]) ``` The displayed values correspond to the symmetrized band, and not the actual input arguments. I think displaying the symmetrized elements makes more sense here, as this matches the form in the 3-argument `show`.