# Help to reduce number of allocations

**URL:** <https://discourse.julialang.org/t/help-to-reduce-number-of-allocations/19308>\
**Category:** General Usage\
**Created:** [January 5, 2019, 4:46pm UTC](https://discourse.julialang.org/t/help-to-reduce-number-of-allocations/19308 "2019-01-05T16:46:47Z")\
**Posts on this page:** 4\
**Page:** 2

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**Author:** ![Ronis\_BR](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ronis_br/32/50999_2.png) [@Ronis\_BR](https://discourse.julialang.org/u/Ronis_BR)\
**Post date:** [January 6, 2019, 11:51am UTC](https://discourse.julialang.org/t/help-to-reduce-number-of-allocations/19308/21 "2019-01-06T11:51:29Z")

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Hi @DNF,

I took me a while to create a MWE, but I figured out the part of the code that was allocating:

```julia
using LinearAlgebra

function simulate()

    k_max = 6000
    I18 = Matrix{Float64}(I,18,18)
    O3 = zeros(3,3)

    P0 = copy(I18)
    Q = 1e-20I18
    R = diagm(0 => [3e-2, 3e-2, 3e-2, 5e7, 5e7, 5e7])

    Fk_1 = I18

    Hk = [ -I O3 -I I O3 O3;
           -I O3 O3 O3 -I I; ]

    Pu = copy(P0)
    Pp = similar(P0)
    K = zeros(18,6)
    aux = zeros(18,18)

    result = Vector{Float64}(undef,0)
    push!(result, tr(Pu))

    @inbounds for k = 2:k_max
        Pp .= Fk_1*Pu*Fk_1' .+ Q
        K .= Pp*Hk'*pinv(R .+ Hk*Pp*Hk')
        aux .= I - K*Hk
        Pu .= aux*Pp*aux' + K*R*K'

        # Compute and store the result.
        push!(result, tr(Pu))
    end

    result
end

```

which leads to:

```julia-repl
julia> @btime simulate()
  116.695 ms (246202 allocations: 242.91 MiB)

```

EDIT: At least in my attempts, using `mul!` did not help to reduce the allocation here either.

P.S.: I cannot pre-allocate the vector `result` because in the original code the loop can be interrupted if a condition impossible to simulate here is met.

---

<div class="post-metadata">

**Author:** ![Ronis\_BR](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ronis_br/32/50999_2.png) [@Ronis\_BR](https://discourse.julialang.org/u/Ronis_BR)\
**Post date:** [January 6, 2019, 5:04pm UTC](https://discourse.julialang.org/t/help-to-reduce-number-of-allocations/19308/22 "2019-01-06T17:04:13Z")

</div>

Guys,

After analyzing the code with `@timeit` I discovered that I had a function that was allocating a lot:

```julia
skew_matrix(v::AbstractVector{T}) where T<:Real =
    SMatrix{3,3,T,9}( 0, -v[3], +v[2],
                     +v[3], 0, -v[1],
                     -v[2], +v[1], 0 )'

function meas_matrix(s::AbstractVector{T}, b::AbstractVector{T}) where T<:Real
    sx = skew_matrix(s)
    bx = skew_matrix(b)
    O3 = zeros(T,3,3)

    [ -sx O3 -sx I O3 O3;
      -bx O3 O3 O3 -bx I; ]
end

```

It turn out that the problem (50% of the allocation) was happening now due to the `O3`. Since I would need `O3` to depend on the type `T`, I solved this by using `@generated` function:

```julia
@generated function meas_matrix(s::AbstractVector{T}, b::AbstractVector{T}) where T<:Real
    quote
        # These are allocated only when the method is compiled.
        O3 = $(zeros(T,3,3))
        I3 = $(Matrix{T}(I,3,3))

        sx = skew_matrix(s)
        bx = skew_matrix(b)

        return [ -sx O3 -sx I3 O3 O3;
                 -bx O3 O3 O3 -bx I3; ]
    end
end

```

The allocation dropped from 200 MiB to 15 MiB. I could go even further if I defined the matrix element by element, then it goes to 9 MiB, but I do not see any major gains.

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<div class="post-metadata">

**Author:** ![baggepinnen](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/baggepinnen/32/693_2.png) [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)\
**Post date:** [January 6, 2019, 6:24pm UTC](https://discourse.julialang.org/t/help-to-reduce-number-of-allocations/19308/23 "2019-01-06T18:24:25Z")

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Have you checked out FillArrays.jl? It would drop allocations without resorting to @generated

---

<div class="post-metadata">

**Author:** ![Ronis\_BR](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ronis_br/32/50999_2.png) [@Ronis\_BR](https://discourse.julialang.org/u/Ronis_BR)\
**Post date:** [January 6, 2019, 6:28pm UTC](https://discourse.julialang.org/t/help-to-reduce-number-of-allocations/19308/24 "2019-01-06T18:28:08Z")

</div>

Awesome! Thanks, I did not know about this package. It seems very nice!

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