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rdiv! on LU object is much slower than ldiv! #1085
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I benchmarked |
All time seem to be spent in Since it is an adjoint it is iterating there in a cache unfriendly way (row by row). Not sure if that is the full answer. |
Why would it be calling |
The problem is that LAPACK's With the following new functions julia> LinearAlgebra.ldiv!(A::LinearAlgebra.AdjointFactorization{T,<:LU{T,<:StridedMatrix}}, B::Adjoint{T,<:StridedVecOrMat{T}}) where {T<:LinearAlgebra.BlasComplex} = LAPACK.getrs!('C', A.parent.factors, A.parent.ipiv, copy(B))
julia> LinearAlgebra.ldiv!(A::LinearAlgebra.TransposeFactorization{T,<:LU{T,<:StridedMatrix}}, B::Transpose{T,<:StridedVecOrMat{T}}) where {T<:LinearAlgebra.BlasFloat} = LAPACK.getrs!('T', A.parent.factors, A.parent.ipiv, copy(B)) which are in line with the implementations of julia> A = rand(1000,1000); @btime inv($A); @btime inv2($A); @btime inv3($A);
20.489 ms (5 allocations: 8.13 MiB)
30.846 ms (5 allocations: 15.27 MiB)
32.751 ms (7 allocations: 22.90 MiB) However, this requires a copy (mainly memory impact): julia> @btime copy(A);
242.988 μs (2 allocations: 7.63 MiB) |
Update: As indicated by @dkarrasch in the comments of the now-closed PR JuliaLang/julia#55760, this is not a missing functionality issue, but a dispatch issue. See JuliaLang/julia#55764 for a possible solution. |
Indeed. Unfortunately, I have very little time at the moment, so if somebody could debug the "lu of tridiagonal" case in that PR (everything else is working just fine), that would be awesome! |
From this post, I'm finding that
rdiv!
on LU objects (added in JuliaLang/julia#31285) is much slower thanldiv!
.For example:
gives
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