# Reduce allocations LinearSolve

**URL:** <https://discourse.julialang.org/t/reduce-allocations-linearsolve/104141>\
**Category:** Performance\
**Created:** [September 22, 2023, 10:03am UTC](https://discourse.julialang.org/t/reduce-allocations-linearsolve/104141 "2023-09-22T10:03:38Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![Kieran\_Marray](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kieran_marray/32/35686_2.png) [@Kieran\_Marray](https://discourse.julialang.org/u/Kieran_Marray)\
**Post date:** [September 22, 2023, 10:03am UTC](https://discourse.julialang.org/t/reduce-allocations-linearsolve/104141/1 "2023-09-22T10:03:38Z")

</div>

Hi - I am trying to solve a linear problem repeatedly using LinearSolve.jl without allocating any new memory by mutating the input and solution arrays. Here is a minimal example

```julia
using LinearAlgebra, LinearSolve, IterativeSolvers, BenchmarkTools

const n = 1000
lhs = rand(n-1) # pre-allocating lhs, rhs
rhs = rand(n-1,n-1)
b_hat = Vector{Float64}(undef, n-1) # pre-allocating results
lin_prob = LinearProblem(rhs, lhs) # setting up the linear problem
lin_solve = init(lin_prob)

function update_b_hat!(b_hat::Vector{Float64}, rhs::Matrix{Float64}, lhs::Vector{Float64},
    lin_solve::LinearSolve.LinearCache{Matrix{Float64}, Vector{Float64}, Vector{Float64}, SciMLBase.NullParameters, Nothing, LU{Float64, Matrix{Float64}}, IterativeSolvers.Identity, IterativeSolvers.Identity, Float64, Nothing})
   lin_solve.A .= rhs
   lin_solve.b .= lhs
   b_hat .= solve(lin_solve).u # 6 allocations in solve()
end
lhs_new = rand(n-1)
rhs_new = rand(n-1,n-1)
update_b_hat!(b_hat, rhs_new, lhs_new, lin_solve)

```

Running the function `update_b_hat!` produces 8 allocations. The allocations are a problem as run this function in an inner loop. Is there a way to update both sides of the linear problem and solve it without making any new allocations?

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<div class="post-metadata">

**Author:** ![Sevi](https://avatars.discourse-cdn.com/v4/letter/s/c67d28/32.png) [@Sevi](https://discourse.julialang.org/u/Sevi)\
**Post date:** [September 22, 2023, 11:17am UTC](https://discourse.julialang.org/t/reduce-allocations-linearsolve/104141/2 "2023-09-22T11:17:54Z")

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I get a `MethodError` when trying to run the code (with the latest versions of `LinearSolve`), because one of the type parameters in the signature doesn’t match. Removing the type annotation of `lin_solve::LinearSolve.LinearCache{...}` and solves this issue and makes the code a lot more readable.

Also, I don’t get any allocations from `update_b_hat!` 🤔

```julia
julia> @btime update_b_hat!($b_hat, $rhs_new, $lhs_new, $lin_solve)
  775.754 μs (0 allocations: 0 bytes)

```

How are you benchmarking the function? And what are the versions of the packages/Julia?

> **versioninfo()**
>
> ```julia
> Julia Version 1.9.3
> Commit bed2cd540a1 (2023-08-24 14:43 UTC)
> Build Info:
> Official https://julialang.org/ release
> Platform Info:
> OS: Linux (x86_64-linux-gnu)
> CPU: 64 × AMD Ryzen Threadripper PRO 3975WX 32-Cores
> WORD_SIZE: 64
> LIBM: libopenlibm
> LLVM: libLLVM-14.0.6 (ORCJIT, znver2)
> Threads: 1 on 64 virtual cores
> Environment:
> JULIA_PKG_USE_CLI_GIT = true
> JULIA_EDITOR = code
> JULIA_NUM_THREADS = 
> JULIA_IMAGE_THREADS = 1
> 
> ```

> **pkg\> status**
>
> ```julia
> Status `/tmp/jl_fVsy9u/Project.toml`
> [6e4b80f9] BenchmarkTools v1.3.2
> [42fd0dbc] IterativeSolvers v0.9.2
> [7ed4a6bd] LinearSolve v2.6.0
> [37e2e46d] LinearAlgebra
> 
> ```

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<div class="post-metadata">

**Author:** ![Kieran\_Marray](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kieran_marray/32/35686_2.png) [@Kieran\_Marray](https://discourse.julialang.org/u/Kieran_Marray)\
**Post date:** [September 22, 2023, 11:29am UTC](https://discourse.julialang.org/t/reduce-allocations-linearsolve/104141/3 "2023-09-22T11:29:32Z")

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Weird! I use the `@btime` from BenchmarkTools with dollar signs in front of all the arguments. I am using LinearSolve 1.29.1 and Julia 1.7.2

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<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [September 22, 2023, 12:15pm UTC](https://discourse.julialang.org/t/reduce-allocations-linearsolve/104141/4 "2023-09-22T12:15:21Z")

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Julia v1.9 has some of the missing `ldiv!` dispatches required for some cases to further reduce allocations.

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<div class="post-metadata">

**Author:** ![Kieran\_Marray](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kieran_marray/32/35686_2.png) [@Kieran\_Marray](https://discourse.julialang.org/u/Kieran_Marray)\
**Post date:** [September 22, 2023, 2:34pm UTC](https://discourse.julialang.org/t/reduce-allocations-linearsolve/104141/5 "2023-09-22T14:34:52Z")

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Thank you for the quick replies! The issue was the versions of LinearSolve and Julia. When I upgraded past LinearSolve v2.0 and Julia v1.9, I now get no allocations