# Julia is slower than matlab when it comes to matrix diagonalization?

**URL:** <https://discourse.julialang.org/t/julia-is-slower-than-matlab-when-it-comes-to-matrix-diagonalization/108658>\
**Category:** General Usage\
**Tags:** question, eigs, eigenvalue-problem\
**Created:** [January 11, 2024, 3:42am UTC](https://discourse.julialang.org/t/julia-is-slower-than-matlab-when-it-comes-to-matrix-diagonalization/108658 "2024-01-11T03:42:27Z")\
**Posts on this page:** 1\
**Showing post:** 21

<div class="post-metadata">

**Author:** ![PeterSimon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/petersimon/32/25193_2.png) [@PeterSimon](https://discourse.julialang.org/u/PeterSimon)\
**Post date:** [January 12, 2024, 5:08am UTC](https://discourse.julialang.org/t/julia-is-slower-than-matlab-when-it-comes-to-matrix-diagonalization/108658/21 "2024-01-12T05:08:49Z")

</div>

The code is below, reproduced from [this post](https://discourse.julialang.org/t/some-eigenpairs-from-a-large-sparse-nonsymmetric-matrix-julia-vs-matlab/93742/14):

```julia
using ArnoldiMethod, LinearAlgebra, LinearMaps

PQ = P*Q

# Factorizes A and builds a linear map that applies inv(A) to a vector.
function construct_linear_map(A)
    F = factorize(A - ev*I)
    LinearMap{eltype(A)}((y, x) -> ldiv!(y, F, x), size(A,1), ismutating=true)
end

function rerun_ArnoldiMethod(n=1, PQ=PQ)
    Threads.nthreads() == n || error("Restart Julia with -t$n")
    BLAS.set_num_threads(n)
    println("ArnoldiMethod $n Threads:")
    @time begin
        decomp, history = partialschur(construct_linear_map(PQ), nev=NMODES, tol=1e-14, restarts=300, which=LM())
        D2, Exy = partialeigen(decomp)
    end
    println(history)
    D2 = inv.(D2) .+ ev
    @show D2
end

```

I’m sorry but I don’t have the time to dig up and test the code to recreate the matrix right now. As stated in my original post in that thread, the matrix `PQ` is a sparse, nonsymmetric, Float64 matrix of order 65274 with 1103319 stored entries.  
`ev` is a scalar with value `-12.25`.

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