Unwrap parent in triangular broadcast #55604
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This PR may be simplified quite a bit after #55626, as processing the structured matrices may not be necessary. |
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This provides most of the benefits seen in #55604. The simpler implementation appears to help with branch-prediction in inferring the zero elements of the structured matrices. The improved performance as a consequence: ```julia julia> using LinearAlgebra julia> U = UpperTriangular(rand(3000,3000)); D = Diagonal(rand(size(U,1))); julia> @Btime $U .+ $D; 23.405 ms (3 allocations: 68.66 MiB) # nightly 15.266 ms (3 allocations: 68.66 MiB) # This PR ``` --------- Co-authored-by: Matt Bauman <[email protected]>
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This provides most of the benefits seen in #55604. The simpler implementation appears to help with branch-prediction in inferring the zero elements of the structured matrices. The improved performance as a consequence: ```julia julia> using LinearAlgebra julia> U = UpperTriangular(rand(3000,3000)); D = Diagonal(rand(size(U,1))); julia> @Btime $U .+ $D; 23.405 ms (3 allocations: 68.66 MiB) # nightly 15.266 ms (3 allocations: 68.66 MiB) # This PR ``` --------- Co-authored-by: Matt Bauman <[email protected]>
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This provides most of the benefits seen in JuliaLang/julia#55604. The simpler implementation appears to help with branch-prediction in inferring the zero elements of the structured matrices. The improved performance as a consequence: ```julia julia> using LinearAlgebra julia> U = UpperTriangular(rand(3000,3000)); D = Diagonal(rand(size(U,1))); julia> @Btime $U .+ $D; 23.405 ms (3 allocations: 68.66 MiB) # nightly 15.266 ms (3 allocations: 68.66 MiB) # This PR ``` --------- Co-authored-by: Matt Bauman <[email protected]>
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We have moved the LinearAlgebra stdlib to an external repo: https://github.com/JuliaLang/LinearAlgebra.jl @jishnub If you think that this PR is still relevant, please open a new PR on the LinearAlgebra.jl repo. |
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This replaces
AbstractTriangularmatrices by their parents in certain broadcast operations, where we only loop over the filled half. We also replaceDiagonal/Bidiagonal/Tridiaognal/SymTridiagonalmatrices by the corresponding zeros away from the bands. As a consequence, this removes branching in the indexing operations in the broadcast, which improves performance considerably.Also
Most of the performance gain comes from replacing the
Diagonalbyzero(eltype(D))in the broadcasting. It's a bit surprising that branch-prediction doesn't do this already.