# Linear solver \\(A, B) performance vs Matlab A\\b

**URL:** <https://discourse.julialang.org/t/linear-solver-a-b-performance-vs-matlab-a-b/2082>\
**Category:** General Usage\
**Created:** [February 13, 2017, 2:23pm UTC](https://discourse.julialang.org/t/linear-solver-a-b-performance-vs-matlab-a-b/2082 "2017-02-13T14:23:03Z")\
**Posts on this page:** 13\
**Page:** 2

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**Author:** ![roryd](https://avatars.discourse-cdn.com/v4/letter/r/839c29/32.png) [@roryd](https://discourse.julialang.org/u/roryd)\
**Post date:** [February 21, 2017, 4:35am UTC](https://discourse.julialang.org/t/linear-solver-a-b-performance-vs-matlab-a-b/2082/21 "2017-02-21T04:35:11Z")

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@Ralph_Smith indeed – my use cases are all artificial! But that’s because I’m working on a modification to L\_1 / L\_2 regularized regression, and I’m just generating fake data to test with. Thanks for the pointer to some more robust methods. The coordinate descent approach seems like a nice place to live in terms interpretability (important for novices like me) and accessibility to modifications that make L\_1 and L\_2 penalties easy to add without making the matrices bigger, but I’ll definitely take a look at those other methods.

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**Author:** ![goldfita](https://avatars.discourse-cdn.com/v4/letter/g/4491bb/32.png) [@goldfita](https://discourse.julialang.org/u/goldfita)\
**Post date:** [May 17, 2017, 1:56am UTC](https://discourse.julialang.org/t/linear-solver-a-b-performance-vs-matlab-a-b/2082/22 "2017-05-17T01:56:10Z")

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How about Julia vs Julia? I was surprised to discover my 0.6-rc is 10x slower than 0.5 official version in at least one use case. It’s compiled without GPL libs, but I can’t find where it’s calling into an optimized library. I believe it’s calling lufact! in lu.jl. Not sure what else is different between the two versions.

```julia
versioninfo()
Julia Version 0.5.1
Commit 6445c82 (2017-03-05 13:25 UTC)
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: Intel(R) Core(TM) i7-6820HQ CPU @ 2.70GHz
  WORD_SIZE: 64
  BLAS: libopenblas (USE64BITINT DYNAMIC_ARCH NO_AFFINITY Haswell)
  LAPACK: libopenblas64_
  LIBM: libopenlibm
  LLVM: libLLVM-3.7.1 (ORCJIT, broadwell)

a=randn(90,90);
b=randn(90);
@time for i=1:10000; a\b; end
  0.864465 seconds (80.00 k allocations: 635.529 MB, 6.92% gc time)
@which lufact(a)
lufact{T<:AbstractFloat}(A::Union{AbstractArray{Complex{T},2},AbstractArray{T,2}}) at linalg\lu.jl:72

versioninfo()
Julia Version 0.6.0-rc1.3
Commit c302d75d95 (2017-05-14 09:56 UTC)
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: Intel(R) Core(TM) i7-6820HQ CPU @ 2.70GHz
  WORD_SIZE: 64
  BLAS: libopenblas (USE64BITINT DYNAMIC_ARCH NO_AFFINITY Haswell)
  LAPACK: libopenblas64_
  LIBM: libopenlibm
  LLVM: libLLVM-3.9.1 (ORCJIT, skylake)
@time for i=1:10000; a\b; end
  8.576880 seconds (80.00 k allocations: 635.529 MiB, 0.86% gc time)
@which lufact(a)
lufact(A::Union{AbstractArray{Complex{T},2}, AbstractArray{T,2}}) where T<:AbstractFloat in Base.LinAlg at linalg\lu.jl:81

```

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**Author:** ![fredrikekre](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fredrikekre/32/1688_2.png) [@fredrikekre](https://discourse.julialang.org/u/fredrikekre)\
**Post date:** [May 17, 2017, 9:42am UTC](https://discourse.julialang.org/t/linear-solver-a-b-performance-vs-matlab-a-b/2082/23 "2017-05-17T09:42:52Z")

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You should’t benchmark in global scope like that [https://docs.julialang.org/en/stable/manual/performance-tips/](https://docs.julialang.org/en/stable/manual/performance-tips/)

julia 0.5:

```julia
julia> using BenchmarkTools

julia> a = randn(90,90); b = randn(90);

julia> @btime $a \ $ b;
  103.155 μs (8 allocations: 65.08 KiB)

```

julia 0.6:

```julia
julia> using BenchmarkTools

julia> a = randn(90,90); b = randn(90);

julia> @btime $a \ $ b;
  100.378 μs (8 allocations: 65.08 KiB)

```

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**Author:** ![goldfita](https://avatars.discourse-cdn.com/v4/letter/g/4491bb/32.png) [@goldfita](https://discourse.julialang.org/u/goldfita)\
**Post date:** [May 17, 2017, 3:56pm UTC](https://discourse.julialang.org/t/linear-solver-a-b-performance-vs-matlab-a-b/2082/24 "2017-05-17T15:56:33Z")

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> [@fredrikekre](#):
>
> @btime a \ b;

Thanks for reminding me of the hazards of global scope. I tried it your way, but the relative performance is about the same.

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**Author:** ![goldfita](https://avatars.discourse-cdn.com/v4/letter/g/4491bb/32.png) [@goldfita](https://discourse.julialang.org/u/goldfita)\
**Post date:** [May 17, 2017, 5:00pm UTC](https://discourse.julialang.org/t/linear-solver-a-b-performance-vs-matlab-a-b/2082/25 "2017-05-17T17:00:02Z")

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I believe the culprit may be this line.

```julia
 lpt = LAPACK.getrf!(A)

# v0.6
 @code_lowered LAPACK.getrf!(a)
...
$(Expr(:foreigncall, :((Core.tuple)(:dgetrf_64_, Base.LinAlg.LAPACK.liblapack)), Void, svec(Ptr{Int64}, Ptr{Int64}, Ptr{Float64}, Ptr{Int64}, Ptr{Int64}, Ptr{Int64}), :(&((Base.ptr_arg_unsafe_convert)((Core.apply_type)(Base.LinAlg.LAPACK.Ptr, Base.LinAlg.LAPACK.BlasInt), SSAValue(3)))), SSAValue(3), :(&((Base.ptr_arg_unsafe_convert)((Core.apply_type)(Base.LinAlg.LAPACK.Ptr, Base.LinAlg.LAPACK.BlasInt), SSAValue(4)))), SSAValue(4), :((Base.unsafe_convert)((Core.apply_type)(Base.LinAlg.LAPACK.Ptr, Base.LinAlg.LAPACK.Float64), SSAValue(5))), SSAValue(5), :(&((Base.ptr_arg_unsafe_convert)((Core.apply_type)(Base.LinAlg.LAPACK.Ptr, Base.LinAlg.LAPACK.BlasInt), SSAValue(6)))), SSAValue(6), :((Base.unsafe_convert)((Core.apply_type)(Base.LinAlg.LAPACK.Ptr, Base.LinAlg.LAPACK.BlasInt), SSAValue(7))), SSAValue(7), :((Base.unsafe_convert)((Core.apply_type)(Base.LinAlg.LAPACK.Ptr, Base.LinAlg.LAPACK.BlasInt), SSAValue(8))), SSAValue(8))) # line 538:

# v0.5
 @code_lowered LAPACK.getrf!(a)
...
 (Core.ccall)((Core.tuple)(:dgetrf_64_,Base.LinAlg.LAPACK.liblapack),Base.LinAlg.LAPACK.Void,(Core.svec)((Core.apply_type)(Base.LinAlg.LAPACK.Ptr,Base.LinAlg.LAPACK.BlasInt),(Core.apply_type)(Base.LinAlg.LAPACK.Ptr,Base.LinAlg.LAPACK.BlasInt),(Core.apply_type)(Base.LinAlg.LAPACK.Ptr,Base.LinAlg.LAPACK.Float64),(Core.apply_type)(Base.LinAlg.LAPACK.Ptr,Base.LinAlg.LAPACK.BlasInt),(Core.apply_type)(Base.LinAlg.LAPACK.Ptr,Base.LinAlg.LAPACK.BlasInt),(Core.apply_type)(Base.LinAlg.LAPACK.Ptr,Base.LinAlg.LAPACK.BlasInt)),&((Base.ptr_arg_unsafe_convert)((Core.apply_type)(Base.LinAlg.LAPACK.Ptr,Base.LinAlg.LAPACK.BlasInt),SSAValue(3))),SSAValue(3),&((Base.ptr_arg_unsafe_convert)((Core.apply_type)(Base.LinAlg.LAPACK.Ptr,Base.LinAlg.LAPACK.BlasInt),SSAValue(4))),SSAValue(4),(Base.unsafe_convert)((Core.apply_type)(Base.LinAlg.LAPACK.Ptr,Base.LinAlg.LAPACK.Float64),SSAValue(5)),SSAValue(5),&((Base.ptr_arg_unsafe_convert)((Core.apply_type)(Base.LinAlg.LAPACK.Ptr,Base.LinAlg.LAPACK.BlasInt),SSAValue(6))),SSAValue(6),(Base.unsafe_convert)((Core.apply_type)(Base.LinAlg.LAPACK.Ptr,Base.LinAlg.LAPACK.BlasInt),SSAValue(7)),SSAValue(7),(Base.unsafe_convert)((Core.apply_type)(Base.LinAlg.LAPACK.Ptr,Base.LinAlg.LAPACK.BlasInt),SSAValue(8)),SSAValue(8)) # line 536:

```

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<div class="post-metadata">

**Author:** ![kristoffer.carlsson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kristoffer.carlsson/32/22_2.png) [@kristoffer.carlsson](https://discourse.julialang.org/u/kristoffer.carlsson)\
**Post date:** [May 17, 2017, 5:30pm UTC](https://discourse.julialang.org/t/linear-solver-a-b-performance-vs-matlab-a-b/2082/26 "2017-05-17T17:30:50Z")

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How about for larger matrices?

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**Author:** ![goldfita](https://avatars.discourse-cdn.com/v4/letter/g/4491bb/32.png) [@goldfita](https://discourse.julialang.org/u/goldfita)\
**Post date:** [May 17, 2017, 5:55pm UTC](https://discourse.julialang.org/t/linear-solver-a-b-performance-vs-matlab-a-b/2082/27 "2017-05-17T17:55:24Z")

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The performance is 2x better in 0.6 with a 10000x10000 sized matrix. That doesn’t do me any good though, as I need to solve many smaller matrix problems.

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**Author:** ![GunnarFarneback](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gunnarfarneback/32/1827_2.png) [@GunnarFarneback](https://discourse.julialang.org/u/GunnarFarneback)\
**Post date:** [May 18, 2017, 11:17am UTC](https://discourse.julialang.org/t/linear-solver-a-b-performance-vs-matlab-a-b/2082/28 "2017-05-18T11:17:13Z")

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How does this compare?

```julia
@btime LinAlg.generic_lufact!(copy(a), Val{true}) \ b

```

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**Author:** ![tkelman](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tkelman/32/692_2.png) [@tkelman](https://discourse.julialang.org/u/tkelman)\
**Post date:** [May 18, 2017, 3:54pm UTC](https://discourse.julialang.org/t/linear-solver-a-b-performance-vs-matlab-a-b/2082/29 "2017-05-18T15:54:40Z")

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Try on nightly or rc2, there was a little issue with ccall lowering that Jeff just fixed.

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**Author:** ![goldfita](https://avatars.discourse-cdn.com/v4/letter/g/4491bb/32.png) [@goldfita](https://discourse.julialang.org/u/goldfita)\
**Post date:** [May 18, 2017, 4:40pm UTC](https://discourse.julialang.org/t/linear-solver-a-b-performance-vs-matlab-a-b/2082/30 "2017-05-18T16:40:10Z")

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Doing it this way

```julia
@btime LinAlg.generic_lufact!(copy(a), Val{true}) \ b

```

v0.5 is 3x slower and v0.6 is 2-3x faster; they have about the same run-time. I never got through the larger matrix test; it was taking too long.

I tried rc2 – no improvement.

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**Author:** ![kristoffer.carlsson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kristoffer.carlsson/32/22_2.png) [@kristoffer.carlsson](https://discourse.julialang.org/u/kristoffer.carlsson)\
**Post date:** [May 18, 2017, 5:30pm UTC](https://discourse.julialang.org/t/linear-solver-a-b-performance-vs-matlab-a-b/2082/31 "2017-05-18T17:30:50Z")

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The fact that large matrices are faster and “small” matrices are slower (90 x 90 is way larger than the ccall overhead could explain for) strongly suggests there is a difference in the build configuration of the lapack library.

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**Author:** ![goldfita](https://avatars.discourse-cdn.com/v4/letter/g/4491bb/32.png) [@goldfita](https://discourse.julialang.org/u/goldfita)\
**Post date:** [May 21, 2017, 2:32pm UTC](https://discourse.julialang.org/t/linear-solver-a-b-performance-vs-matlab-a-b/2082/32 "2017-05-21T14:32:42Z")

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For some reason, I didn’t get an email notification of your post. For what it’s worth, here’s my Make.user. There are no other configuration changes. I installed a second version of cygwin just for this build that has only the packages required.

```julia
XC_HOST = x86_64-w64-mingw32
USE_GPL_LIBS = 0
MARCH = native

```

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<div class="post-metadata">

**Author:** ![goldfita](https://avatars.discourse-cdn.com/v4/letter/g/4491bb/32.png) [@goldfita](https://discourse.julialang.org/u/goldfita)\
**Post date:** [May 21, 2017, 11:34pm UTC](https://discourse.julialang.org/t/linear-solver-a-b-performance-vs-matlab-a-b/2082/33 "2017-05-21T23:34:48Z")

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If someone can point me to the relevant file(s), I can poke around and maybe narrow the problem down.

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