julia

e33c6a85 - Specialize adding/subtracting mixed Upper/LowerTriangular (#56149)

Specialize adding/subtracting mixed Upper/LowerTriangular (#56149) Fixes https://github.com/JuliaLang/julia/issues/56134 After this, ```julia julia> using LinearAlgebra julia> A = hermitianpart(rand(4, 4)) 4×4 Hermitian{Float64, Matrix{Float64}}: 0.387617 0.277226 0.67629 0.60678 0.277226 0.894101 0.388416 0.489141 0.67629 0.388416 0.100907 0.619955 0.60678 0.489141 0.619955 0.452605 julia> B = UpperTriangular(A) 4×4 UpperTriangular{Float64, Hermitian{Float64, Matrix{Float64}}}: 0.387617 0.277226 0.67629 0.60678 ⋅ 0.894101 0.388416 0.489141 ⋅ ⋅ 0.100907 0.619955 ⋅ ⋅ ⋅ 0.452605 julia> B - B' 4×4 Matrix{Float64}: 0.0 0.277226 0.67629 0.60678 -0.277226 0.0 0.388416 0.489141 -0.67629 -0.388416 0.0 0.619955 -0.60678 -0.489141 -0.619955 0.0 ``` This preserves the band structure of the parent, if any: ```julia julia> U = UpperTriangular(Diagonal(ones(4))) 4×4 UpperTriangular{Float64, Diagonal{Float64, Vector{Float64}}}: 1.0 0.0 0.0 0.0 ⋅ 1.0 0.0 0.0 ⋅ ⋅ 1.0 0.0 ⋅ ⋅ ⋅ 1.0 julia> U - U' 4×4 Diagonal{Float64, Vector{Float64}}: 0.0 ⋅ ⋅ ⋅ ⋅ 0.0 ⋅ ⋅ ⋅ ⋅ 0.0 ⋅ ⋅ ⋅ ⋅ 0.0 ``` This doesn't fully work with partly initialized matrices, and would need https://github.com/JuliaLang/julia/pull/55312 for that. The abstract triangular methods now construct matrices using `similar(parent(U), size(U))` so that the destinations are fully mutable. ```julia julia> @invoke B::LinearAlgebra.AbstractTriangular - B'::LinearAlgebra.AbstractTriangular 4×4 Matrix{Float64}: 0.0 0.277226 0.67629 0.60678 -0.277226 0.0 0.388416 0.489141 -0.67629 -0.388416 0.0 0.619955 -0.60678 -0.489141 -0.619955 0.0 ``` --------- Co-authored-by: Daniel Karrasch <daniel.karrasch@posteo.de>