# How to add two symmetric matrices inplace?

**URL:** <https://discourse.julialang.org/t/how-to-add-two-symmetric-matrices-inplace/55849>\
**Category:** General Usage\
**Tags:** question, linearalgebra\
**Created:** [February 23, 2021, 1:59pm UTC](https://discourse.julialang.org/t/how-to-add-two-symmetric-matrices-inplace/55849 "2021-02-23T13:59:04Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![jishnub](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jishnub/32/33620_2.png) [@jishnub](https://discourse.julialang.org/u/jishnub)\
**Post date:** [February 23, 2021, 1:59pm UTC](https://discourse.julialang.org/t/how-to-add-two-symmetric-matrices-inplace/55849/1 "2021-02-23T13:59:04Z")

</div>

Symmetric matrices do not permit editing off-diagonal elements. I have two matrices `S1` and `S2` and I’m trying to evaluate `S1 + S2` and save the result into `S2`. Typically `S2 .+= S1` would achieve this but this doesn’t work for Symmetric matrices.

```julia
julia> S1 = Symmetric(ones(3,3), :U);

julia> S2 = similar(S1);

julia> S2 .+= S1
ERROR: ArgumentError: Cannot set a non-diagonal index in a symmetric matrix
Stacktrace:
  [1] setindex!
    @ /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.7/LinearAlgebra/src/symmetric.jl:225 [inlined]
  [2] _setindex!
    @ ./abstractarray.jl:1297 [inlined]
  [3] setindex!
    @ ./abstractarray.jl:1267 [inlined]
  [4] macro expansion
    @ ./broadcast.jl:983 [inlined]
  [5] macro expansion
    @ ./simdloop.jl:77 [inlined]
  [6] copyto!
    @ ./broadcast.jl:982 [inlined]
  [7] copyto!
    @ ./broadcast.jl:935 [inlined]
  [8] materialize!
    @ ./broadcast.jl:893 [inlined]
  [9] materialize!(dest::Symmetric{Float64, Matrix{Float64}}, bc::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{2}, Nothing, typeof(+), Tuple{Symmetric{Float64, Matrix{Float64}}, Symmetric{Float64, Matrix{Float64}}}})
    @ Base.Broadcast ./broadcast.jl:890
 [10] top-level scope
    @ REPL[24]:1

```

Strangely assignment works:

```julia
julia> S2 .= S1
3×3 Symmetric{Float64, Matrix{Float64}}:
 1.0 1.0 1.0
 1.0 1.0 1.0
 1.0 1.0 1.0

julia> all(isone, S2)
true

```

so perhaps one may set off-diagonal elements after all?

I realize that there’s a way around this by using the parent arrays:

```julia
julia> parent(S2) .= 0

julia> parent(S2) .+= parent(S1);

julia> S2
3×3 Symmetric{Float64, Matrix{Float64}}:
 1.0 1.0 1.0
 1.0 1.0 1.0
 1.0 1.0 1.0

```

but this seems to be an uncessary foray into the internals.

Also

```julia
julia> S2 += S1
3×3 Symmetric{Float64, Matrix{Float64}}:
 3.0 2.0 2.0
 2.0 2.0 2.0
 2.0 2.0 2.0

```

works as expected, but this creates a new binding. This is not what I want.

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<div class="post-metadata">

**Author:** ![jishnub](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jishnub/32/33620_2.png) [@jishnub](https://discourse.julialang.org/u/jishnub)\
**Post date:** [February 24, 2021, 5:24am UTC](https://discourse.julialang.org/t/how-to-add-two-symmetric-matrices-inplace/55849/2 "2021-02-24T05:24:02Z")

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Related issues: [#38055](https://github.com/JuliaLang/julia/issues/38055), [#32722](https://github.com/JuliaLang/julia/issues/32722)