Specialize adding/subtracting mixed Upper/LowerTriangular #56149
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jishnub
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linear algebra
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The broken tests here would be fixed by #55312, so one of these should be rebased after the other is merged. |
dkarrasch
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Oct 17, 2024
dkarrasch
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Oct 17, 2024
Co-authored-by: Daniel Karrasch <[email protected]>
jishnub
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Oct 21, 2024
KristofferC
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Fixes #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 #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 <[email protected]>
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Fixes #56134
After this,
This preserves the band structure of the parent, if any:
This doesn't fully work with partly initialized matrices, and would need #55312 for that.
The abstract triangular methods now construct matrices using
similar(parent(U), size(U))so that the destinations are fully mutable.