Why is work with Q in qr() is so expensive?

General Usage Performance
, ,
6

I have also responded in the issue, but let me repeat here for convenience:

julia> for i in 1:100:500

           A = randn(i,i)
           println("Size = $i")
           printstyled("Time took for q : ", color=:green)
           @time Q = qr(A).Q
           printstyled("Time took for Q*1 : ", color=:red)
           @time Q = Q*1
           println("")
       end
Size = 1
Time took for q :   0.000008 seconds (5 allocations: 352 bytes)
Time took for Q*1 :   0.000010 seconds (2 allocations: 192 bytes)

Size = 101
Time took for q :   0.000418 seconds (8 allocations: 136.922 KiB)
Time took for Q*1 :   0.000158 seconds (4 allocations: 159.656 KiB)

Size = 201
Time took for q :   0.000888 seconds (8 allocations: 429.109 KiB)
Time took for Q*1 :   0.000433 seconds (4 allocations: 631.531 KiB)

Size = 301
Time took for q :   0.001847 seconds (8 allocations: 877.547 KiB)
Time took for Q*1 :   0.001077 seconds (4 allocations: 1.383 MiB)

Size = 401
Time took for q :   0.003631 seconds (8 allocations: 1.447 MiB)
Time took for Q*1 :   0.003361 seconds (4 allocations: 2.454 MiB)

julia> @which qr(randn(2,2)).Q * 1
*(A::LinearAlgebra.AbstractQ, b::Number) in LinearAlgebra at /Users/crstnbr/repos/julia/usr/share/julia/stdlib/v1.7/LinearAlgebra/src/qr.jl:618

julia> versioninfo()
Julia Version 1.7.0-DEV.915
Commit 2ba139c48e* (2021-04-13 04:20 UTC)
Platform Info:
  OS: macOS (x86_64-apple-darwin20.3.0)
  CPU: Intel(R) Core(TM) i7-9750H CPU @ 2.60GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-11.0.1 (ORCJIT, skylake)
Environment:
  JULIA_EDITOR = subl
  JULIA_NUM_THREADS = 6
  JULIA_PKG_SERVER = eu-central.pkg.julialang.org

So this issue seems to be fixed on master (Julia 1.7-DEV)

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