Unwrap triangular matrices in broadcast #1332
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jishnub
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In broadcasting over triangular matrices, we loop only over the stored indices. For these indices, indexing into a triangular matrix is equivalent to indexing into its parent. We may therefore replace an `UpperOrLowerTriangular` matrix by its parent, which removes the branch in `getindex`. This improves performance: ```julia julia> L = LowerTriangular(zeros(600,600)); julia> L2 = copy(L); julia> @Btime broadcast!(+, $L2, $L, $L); 161.176 μs (0 allocations: 0 bytes) # master 80.894 μs (0 allocations: 0 bytes) # this PR ``` This replacement is performed recursively on a `Broadcasted` object by looping over its `args`, and non-triangular elements are left untouched. Only `UpperOrLowerTriangular` matrices will be replaced by their `parent`s. (cherry picked from commit 5165fd3)
jishnub
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Backported PRs: - [x] #1209 <!-- Remove `LinearAlgebra` qualifications in `cholesky.jl` --> - [x] #1230 <!-- Avoid materializing `diag` in `Diagonal` `kron` --> - [x] #1240 <!-- Reduce `stable_muladdmul` branches in `generic matvecmul!` --> - [x] #1247 <!-- fix dispatch to herk --> - [x] #1255 <!-- use smaller matrix size in `peakflops` on 32-bit --> - [x] #1310 <!-- Only `@noinline` error path in `matmul_size_check` --> - [x] #1267 <!-- Refine column ranges in `_isbanded_impl` --> - [x] #1320 <!-- Copy matrices in `triu`/`tril` if no zero exists for the `eltype` --> - [x] #1324 <!-- Fix empty `Tridiagonal` broadcast --> - [x] #1327 <!-- `iszero` check in hessenberg setindex --> - [x] #1326 <!-- Fix multiplication with empty `HessenbergQ` --> - [x] #1332 <!-- Unwrap triangular matrices in broadcast --> - [x] #1337 <!-- Change `1:size` to `axes` in bidiag mul --> - [x] #1342 <!-- `Char` uplo in `Bidiagonal` constructor --> - [x] #1344 <!-- Update the docstring of ldiv! --> - [x] #1335 <!-- Test: prune old LA based on ENV variable --> - [x] #1346 <!-- Fix scaling unit triangular matrices --> - [x] #1355 <!-- Add compat notice for `diagview` --> - [x] #1349 <!-- Prune `LinearAlgebra` module in ambiguity test --> Contains multiple commits, manual intervention needed: - [x] #1238 <!-- Ensure positive-definite matrix in lapack posv test --> - [x] #1298 <!-- Add `diagm` example --> - [x] #1312 <!-- WIP: Try use method deletion instead of custom sysimage --> - [x] #1333 <!-- Make `fillstored!` public --> - [x] #1331 <!-- Document SingularException throw for inv(::AbstractMatrix) --> - [x] #1350 <!-- Fix copy for partly initialized unit triangular --> Non-merged PRs with backport label: - [x] #1352 <!-- log for dense diagonal matrix with negative elements --> - [ ] #1305 <!-- Bounds-checking in triangular indexing branches --> --------- Co-authored-by: Mateus Araújo <[email protected]> Co-authored-by: Jeff Bezanson <[email protected]> Co-authored-by: Steven G. Johnson <[email protected]> Co-authored-by: WalterMadelim <[email protected]> Co-authored-by: Kristoffer Carlsson <[email protected]> Co-authored-by: Daniel Karrasch <[email protected]> Co-authored-by: Michael Abbott <[email protected]>
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In broadcasting over triangular matrices, we loop only over the stored indices. For these indices, indexing into a triangular matrix is equivalent to indexing into its parent. We may therefore replace an
UpperOrLowerTriangularmatrix by its parent, which removes the branch ingetindex. This improves performance:This replacement is performed recursively on a
Broadcastedobject by looping over itsargs, and non-triangular elements are left untouched. OnlyUpperOrLowerTriangularmatrices will be replaced by theirparents.