# Large Matrix Takes Forever
**URL:** https://discourse.julialang.org/t/large-matrix-takes-forever/21328
**Category:** Performance
**Tags:** linearalgebra
**Created:** [March 1, 2019, 3:23am UTC](https://discourse.julialang.org/t/large-matrix-takes-forever/21328 "2019-03-01T03:23:18Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@olabaz](https://discourse.julialang.org/u/olabaz)
#### Post date: [March 1, 2019, 3:23am UTC](https://discourse.julialang.org/t/large-matrix-takes-forever/21328/1 "2019-03-01T03:23:18Z")
Hi, I am new to Julia and I am writing a program that makes a random matrix drawn from the Haar distribution. It works fine for small matrices ~200x200 but when I try for 1000x1000 the program takes a very long time to run. I am not sure what the issue is here.
```julia
using Random, LinearAlgebra
using Plots
function mkHaar(dimMat)
#initialize random number generatore and create complex 4x4 normal random matrix
rng = MersenneTwister()
rndMat = randn(rng, ComplexF64, (dimMat, dimMat))
Z = qr(rndMat)
L = Diagonal(Z.R)/abs.(Diagonal(Z.R))
rndHaar = Z.Q*L
#We can check to see that rndHaar is Unitary
#println(adjoint(rndHaar)*rndHaar)
#and that the eigenvalue phases are uniformly distributed
EV = eigvals(rndHaar)
phaseEV = angle.(EV)
#Make histogram
gr(size = (300,300), legend = false)
#create binning breaks
binbrks = range(-pi, stop = pi, length = 25)
p = histogram(phaseEV,bins=binbrks)
display(p)
end
```
---
### Author:  [@rdeits](https://discourse.julialang.org/u/rdeits)
#### Post date: [March 1, 2019, 4:17am UTC](https://discourse.julialang.org/t/large-matrix-takes-forever/21328/2 "2019-03-01T04:17:28Z")
It looks like matrix multiplication with `Z.Q` (which is not actually a plain matrix but a special type for the result of the QR factorization) is very slow because it ends up calling the `getindex` function here: [julia/qr.jl at 8639dc1dbfb9d0a8df50e1eb95e68cc6be880bd3 · JuliaLang/julia · GitHub](https://github.com/JuliaLang/julia/blob/8639dc1dbfb9d0a8df50e1eb95e68cc6be880bd3/stdlib/LinearAlgebra/src/qr.jl#L515-L521) which looks pretty slow to me.
You can get around this by just copying it to a matrix first:
```julia
rndHaar = Matrix(Z.Q) * L
```
There’s probably a better way to fix this in Julia itself, but I don’t know that part of the code well enough.
---
### Author:  [@jebej](https://discourse.julialang.org/u/jebej)
#### Post date: [March 1, 2019, 10:56pm UTC](https://discourse.julialang.org/t/large-matrix-takes-forever/21328/3 "2019-03-01T22:56:21Z")
Here’s an implementation that will work (you can remove the two `Compat.` prefixes if you are on 1.0):
>
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### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [March 2, 2019, 4:34am UTC](https://discourse.julialang.org/t/large-matrix-takes-forever/21328/4 "2019-03-02T04:34:42Z")
> [@rdeits](#):
>
> There’s probably a better way to fix this in Julia itself, but I don’t know that part of the code well enough.
There is a fast method for multiplying the special “Q” matrix type by a `StridedMatrix`: [https://github.com/JuliaLang/julia/blob/master/stdlib/LinearAlgebra/src/qr.jl#L567](https://github.com/JuliaLang/julia/blob/master/stdlib/LinearAlgebra/src/qr.jl#L567)
but this doesn’t get called for multiplying by a `Diagonal` matrix, for which it ends up calling `*(::AbstractMatrix, ::Diagonal)` instead.
To avoid having an explosion of the number of `*(...)` methods we need, it might be nice to have some kind of `ExpensiveIndexing` trait that generic methods can check to see if they need to make a `Matrix` copy before executing indexing-heavy algorithms.
---
### Author:  [@olabaz](https://discourse.julialang.org/u/olabaz)
#### Post date: [March 4, 2019, 5:06pm UTC](https://discourse.julialang.org/t/large-matrix-takes-forever/21328/5 "2019-03-04T17:06:01Z")
Hi,
Thanks for all the replies they were very helpful. For now I think I will just add the Matrix() since it is the simplest but I’ll do some performance checks and see what’s the best way to handle this in the future.