# LU factorization performance issue

**URL:** <https://discourse.julialang.org/t/lu-factorization-performance-issue/82281>\
**Category:** New to Julia\
**Tags:** linearalgebra\
**Created:** [June 5, 2022, 7:36pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281 "2022-06-05T19:36:58Z")\
**Posts on this page:** 20\
**Page:** 1

<div class="post-metadata">

**Author:** ![Abhilash](https://avatars.discourse-cdn.com/v4/letter/a/9fc29f/32.png) [@Abhilash](https://discourse.julialang.org/u/Abhilash)\
**Post date:** [June 5, 2022, 7:36pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/1 "2022-06-05T19:36:58Z")

</div>

I am comparing times taken for LU decomposition and my julia version seems to do badly compared to other language versions. The matrix is a 10000x10000 random dense matrix generated using `DLATMR`.

Calling `dgetrf` (openblas v0.3.20) directly from fortran takes about 3.7s. Python (scipy) takes about 5.4s. Julia for some reason takes about 15s. I include the python and julia codes. I was expecting a similar timing as the other two versions. `BLAS.get_config()` shows that Julia is also calling an OpenBLAS library. I am only measuring the factorization time.

I am trying to find the reason for the apparent slowness of julia in this case.

> **Python Version**
>
> ```python
> import numpy as np
> import struct
> import scipy.linalg as la
> import time
> with open("A.dat", 'rb') as f:
> data=f.read()
> 
> N,= struct.unpack('i', data[:4])
> A= np.frombuffer(data[4:4+8*N*N], dtype=np.float64)
> A= A.reshape((N,N))
> B= np.frombuffer(data[8*N*N+4:], dtype=np.float64)
> print(f"{N=}")
> # print(A)
> # print(B)
> 
> t1= time.time()
> lu,piv= la.lu_factor(A)
> t2=time.time()-t1
> print(f"{t2=}")
> x= la.lu_solve((lu,piv), B)
> print(x[:10])
> print("B-AX==0 ? :",np.allclose(A@x,B))
> 
> ```

> **Julia v1.7.3**
>
> ```julia
> using LinearAlgebra, Statistics;
> print("BLAS thread count: ",BLAS.get_num_threads(),'\n') # is 8
> io=open("A.dat","r")
> N=read(io,Int32)
> A=Array{Float64}(undef,N,N)
> B=Array{Float64}(undef,N,1)
> read!(io,A)
> read!(io,B)
> close(io)
> print(N,"\n")
> 
> t0=time()
> L,U,P=lu(A)
> t1=time()
> 
> X=U\(L\B[P])
> 
> print(t1-t0, '\n')
> print(X[1:10], '\n')
> print(sqrt(mean((B-A*X).^2)))
> 
> ```

The matrix itself is nothing special but its a bit large to share. The config used to generate it is below.

> **dlatmr config**
>
> ```fortran
> M=10000
> N=10000
> SYM='S'
> DIST='U'
> ISEED = [0,47,2000,101]
> MODE = 5
> COND = 1000.0
> DMAX = 100D0
> RSIGN = 'T'
> GRADE = 'N'
> MODEL = 1
> MODER = 1
> PIVTNG = 'N'
> SPARSE = 0.0
> KL = M
> KU = M
> ANORM = 1.0d0
> PACK = 'N'
> LDA = M
> 
> ```

---

<div class="post-metadata">

**Author:** ![jling](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jling/32/212909_2.png) [@jling](https://discourse.julialang.org/u/jling)\
**Post date:** [June 5, 2022, 7:53pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/2 "2022-06-05T19:53:21Z")

</div>

can’t reproduce

```python
In [1]: import numpy as np

In [2]: A = np.random.rand(10000, 10000);

In [3]: import scipy.linalg as la

In [4]: %time la.lu_factor(A)
CPU times: user 39.7 s, sys: 3.03 s, total: 42.8 s
Wall time: 3.15 s

In [5]: %time la.lu_factor(A);
CPU times: user 39.1 s, sys: 3.26 s, total: 42.4 s
Wall time: 3.04 s

```

## Julia

```julia-auto
julia> using LinearAlgebra

julia> const B = rand(10000, 10000);

julia> @time lu(B);
  1.990439 seconds (4 allocations: 763.016 MiB)

julia> @time lu(B);
  1.860999 seconds (4 allocations: 763.016 MiB, 0.38% gc time)

```

---

<div class="post-metadata">

**Author:** ![jling](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jling/32/212909_2.png) [@jling](https://discourse.julialang.org/u/jling)\
**Post date:** [June 5, 2022, 7:54pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/3 "2022-06-05T19:54:28Z")

</div>

> [@Abhilash](#):
>
> ```julia
> A=Array{Float64}(undef,N,N)
> B=Array{Float64}(undef,N,1)
> 
> ```

maybe give these two `const` and also don’t include Julia JIT compile time when benchmarking

---

<div class="post-metadata">

**Author:** ![Abhilash](https://avatars.discourse-cdn.com/v4/letter/a/9fc29f/32.png) [@Abhilash](https://discourse.julialang.org/u/Abhilash)\
**Post date:** [June 5, 2022, 8:04pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/4 "2022-06-05T20:04:30Z")

</div>

Interesting. Something is wrong indeed with my installation of Julia then.

```julia
julia> using LinearAlgebra

julia> const B = rand(10000,10000);

julia> @time lu(B);
 14.362888 seconds (4 allocations: 763.016 MiB, 0.03% gc time)

julia> @time lu(B);
 14.545017 seconds (4 allocations: 763.016 MiB, 0.14% gc time)

```

---

<div class="post-metadata">

**Author:** ![Oscar\_Smith](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/oscar_smith/32/25343_2.png) [@Oscar\_Smith](https://discourse.julialang.org/u/Oscar_Smith)\
**Post date:** [June 5, 2022, 8:04pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/5 "2022-06-05T20:04:51Z")

</div>

What cpu do you have? Also, how did you install Julia?

---

<div class="post-metadata">

**Author:** ![Abhilash](https://avatars.discourse-cdn.com/v4/letter/a/9fc29f/32.png) [@Abhilash](https://discourse.julialang.org/u/Abhilash)\
**Post date:** [June 5, 2022, 8:06pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/6 "2022-06-05T20:06:54Z")

</div>

CPU is i7-1165G7. I installed the 64bit v1.7.3 from [Download Julia](https://julialang.org/downloads/)  
OS is Windows 10

---

<div class="post-metadata">

**Author:** ![ederag](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ederag/32/4106_2.png) [@ederag](https://discourse.julialang.org/u/ederag)\
**Post date:** [June 5, 2022, 8:18pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/7 "2022-06-05T20:18:15Z")

</div>

Maybe you are in a single thread session ?

Single threaded in Pluto:

> 11.503429 seconds (4 allocations: 763.016 MiB)

Multi-threaded in REPL:

> 1.879096 seconds (4 allocations: 763.016 MiB)

---

<div class="post-metadata">

**Author:** ![Abhilash](https://avatars.discourse-cdn.com/v4/letter/a/9fc29f/32.png) [@Abhilash](https://discourse.julialang.org/u/Abhilash)\
**Post date:** [June 5, 2022, 8:22pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/8 "2022-06-05T20:22:21Z")

</div>

I dont think that is the issue. The previous ones were single threaded. This one with 8 threads still shows same result

```julia
julia> Threads.nthreads()
8

julia> const B = rand(10000,10000);

julia> using LinearAlgebra

julia> @time lu(B);
 14.207715 seconds (4 allocations: 763.016 MiB, 0.02% gc time)

julia>

```

---

<div class="post-metadata">

**Author:** ![jling](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jling/32/212909_2.png) [@jling](https://discourse.julialang.org/u/jling)\
**Post date:** [June 5, 2022, 8:24pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/9 "2022-06-05T20:24:46Z")

</div>

how much RAM do you have?

---

<div class="post-metadata">

**Author:** ![Abhilash](https://avatars.discourse-cdn.com/v4/letter/a/9fc29f/32.png) [@Abhilash](https://discourse.julialang.org/u/Abhilash)\
**Post date:** [June 5, 2022, 8:25pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/10 "2022-06-05T20:25:29Z")

</div>

32GB RAM

also thanks for extracting the core problem from my mess of a post haha.

---

<div class="post-metadata">

**Author:** ![jling](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jling/32/212909_2.png) [@jling](https://discourse.julialang.org/u/jling)\
**Post date:** [June 5, 2022, 8:34pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/11 "2022-06-05T20:34:54Z")

</div>

what if you first

```julia
BLAS.set_num_threads(4)

```

?

---

<div class="post-metadata">

**Author:** ![Abhilash](https://avatars.discourse-cdn.com/v4/letter/a/9fc29f/32.png) [@Abhilash](https://discourse.julialang.org/u/Abhilash)\
**Post date:** [June 5, 2022, 8:45pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/12 "2022-06-05T20:45:36Z")

</div>

Doesnt help unfortunately. I tried setting it to 4 and 8. `BLAS.get_num_threads` was 8 by default actually.

---

<div class="post-metadata">

**Author:** ![Abhilash](https://avatars.discourse-cdn.com/v4/letter/a/9fc29f/32.png) [@Abhilash](https://discourse.julialang.org/u/Abhilash)\
**Post date:** [June 5, 2022, 8:48pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/13 "2022-06-05T20:48:35Z")

</div>

I tried to replace Julia’s libopenblas with another one. The replacement was not ilp64. Im going to build an ilp64 version and see if that clarifies things.

---

<div class="post-metadata">

**Author:** ![Abhilash](https://avatars.discourse-cdn.com/v4/letter/a/9fc29f/32.png) [@Abhilash](https://discourse.julialang.org/u/Abhilash)\
**Post date:** [June 5, 2022, 9:03pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/14 "2022-06-05T21:03:40Z")

</div>

The problem is coming from the openblas bundled with the installer (v1.7.3 in this case). Replacing the `libopenblas64_.dll` with a built from source version fixed this problem.

```julia
julia> using LinearAlgebra;

julia> const B = rand(10000,10000);

julia> @time lu(B);
  3.506253 seconds (4 allocations: 763.016 MiB, 0.09% gc time)

julia> @time lu(B);
  3.607796 seconds (4 allocations: 763.016 MiB, 0.07% gc time)

julia>

```

Thanks all for your help!

---

<div class="post-metadata">

**Author:** ![jling](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jling/32/212909_2.png) [@jling](https://discourse.julialang.org/u/jling)\
**Post date:** [June 5, 2022, 9:20pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/15 "2022-06-05T21:20:03Z")

</div>

> [@Abhilash](#):
>
> Changing the OpenBLAS library fixed it

I thought you downloaded from Julia website? which link did you click on

---

<div class="post-metadata">

**Author:** ![Abhilash](https://avatars.discourse-cdn.com/v4/letter/a/9fc29f/32.png) [@Abhilash](https://discourse.julialang.org/u/Abhilash)\
**Post date:** [June 5, 2022, 9:24pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/16 "2022-06-05T21:24:42Z")

</div>

I did install it from the website.  
In trying to find the issue, inside Julia’s installation folder I replaced the openblas library with one that i built from source.

Also I went to file a bug report but this was already there  
[https://github.com/JuliaLang/julia/issues/45090](https://github.com/JuliaLang/julia/issues/45090)

---

<div class="post-metadata">

**Author:** ![jling](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jling/32/212909_2.png) [@jling](https://discourse.julialang.org/u/jling)\
**Post date:** [June 5, 2022, 9:26pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/17 "2022-06-05T21:26:58Z")

</div>

> [@Abhilash](#):
>
> Inside Julia’s installation folder I replaced the openblas library with one that i built from source.

yeah you should have said that as the first thing sir

---

<div class="post-metadata">

**Author:** ![Abhilash](https://avatars.discourse-cdn.com/v4/letter/a/9fc29f/32.png) [@Abhilash](https://discourse.julialang.org/u/Abhilash)\
**Post date:** [June 5, 2022, 9:28pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/18 "2022-06-05T21:28:19Z")

</div>

I think you misunderstood. The one shipped with the installer is borked. The replacement works as expected.

---

<div class="post-metadata">

**Author:** ![jling](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jling/32/212909_2.png) [@jling](https://discourse.julialang.org/u/jling)\
**Post date:** [June 5, 2022, 9:28pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/19 "2022-06-05T21:28:54Z")

</div>

I see, hopefully this is fixed in the upcoming 1.8 as discussed in the github issue.

---

<div class="post-metadata">

**Author:** ![Abhilash](https://avatars.discourse-cdn.com/v4/letter/a/9fc29f/32.png) [@Abhilash](https://discourse.julialang.org/u/Abhilash)\
**Post date:** [June 5, 2022, 11:02pm UTC](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281/20 "2022-06-05T23:02:24Z")

</div>

I just tested with 1.8 rc1 and it works properly out of the box.

[Next page](https://discourse.julialang.org/t/lu-factorization-performance-issue/82281.md?page=2)