# Why is work with Q in qr() is so expensive?
**URL:** https://discourse.julialang.org/t/why-is-work-with-q-in-qr-is-so-expensive/59143
**Category:** Performance
**Tags:** bug, linearalgebra, qr
**Created:** [April 13, 2021, 3:51am UTC](https://discourse.julialang.org/t/why-is-work-with-q-in-qr-is-so-expensive/59143 "2021-04-13T03:51:51Z")
**Posts on this page:** 7
**Page:** 1
### Author:  [@Wei\_Yang](https://discourse.julialang.org/u/Wei_Yang)
#### Post date: [April 13, 2021, 3:51am UTC](https://discourse.julialang.org/t/why-is-work-with-q-in-qr-is-so-expensive/59143/1 "2021-04-13T03:51:51Z")
In the picture below, we can see that it is very efficient to generate a random unitary matrix `Q `using the `qr()` function in LinearAlgebra.
However, if we want to work with the generated `Q`, it appears to be very expensive in memory and time. With size 401 by 401, `Q*1` takes 24 seconds and 1.5 GiB of memory, with size 500 by 500 it appears to take forever.
I wonder what is the reason for this, and how to walk around this issue.
๐Thank you!
---
### Author:  [@AndiMD](https://discourse.julialang.org/u/AndiMD)
#### Post date: [April 13, 2021, 4:38am UTC](https://discourse.julialang.org/t/why-is-work-with-q-in-qr-is-so-expensive/59143/2 "2021-04-13T04:38:44Z")
this is really strange and could be a bug.
Try `Q = convert(Matrix,qr(A).Q) * 1` as a workaround
---
### Author:  [@Wei\_Yang](https://discourse.julialang.org/u/Wei_Yang)
#### Post date: [April 13, 2021, 4:41am UTC](https://discourse.julialang.org/t/why-is-work-with-q-in-qr-is-so-expensive/59143/3 "2021-04-13T04:41:49Z")
Works ! ๐
---
### Author:  [@antoine-levitt](https://discourse.julialang.org/u/antoine-levitt)
#### Post date: [April 13, 2021, 7:14am UTC](https://discourse.julialang.org/t/why-is-work-with-q-in-qr-is-so-expensive/59143/4 "2021-04-13T07:14:24Z")
This appears to hit a very slow fallback:
```julia
julia> @which Q*1
*(A::AbstractArray, B::Number) in Base at arraymath.jl:55
```
Can you open an issue?
---
### Author:  [@Wei\_Yang](https://discourse.julialang.org/u/Wei_Yang)
#### Post date: [April 13, 2021, 7:47am UTC](https://discourse.julialang.org/t/why-is-work-with-q-in-qr-is-so-expensive/59143/5 "2021-04-13T07:47:32Z")
I have just raised an issue [here](https://github.com/JuliaLang/julia/issues/40455).
---
### Author:  [@carstenbauer](https://discourse.julialang.org/u/carstenbauer)
#### Post date: [April 13, 2021, 8:44am UTC](https://discourse.julialang.org/t/why-is-work-with-q-in-qr-is-so-expensive/59143/6 "2021-04-13T08:44:34Z")
I have also responded in the issue, but let me repeat here for convenience:
```julia
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)
---
### Author:  [@ranocha](https://discourse.julialang.org/u/ranocha)
#### Post date: [April 13, 2021, 9:33am UTC](https://discourse.julialang.org/t/why-is-work-with-q-in-qr-is-so-expensive/59143/7 "2021-04-13T09:33:42Z")
For reference: It was fixed in the [PR #39533](https://github.com/JuliaLang/julia/pull/39533).