# Is there a Symmetric Sparse Matrix Implementation in Julia?

**URL:** <https://discourse.julialang.org/t/is-there-a-symmetric-sparse-matrix-implementation-in-julia/91333>\
**Category:** General Usage\
**Tags:** data\_structures, sparse, matrices\
**Created:** [December 7, 2022, 1:56am UTC](https://discourse.julialang.org/t/is-there-a-symmetric-sparse-matrix-implementation-in-julia/91333 "2022-12-07T01:56:01Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![cdelv](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cdelv/32/44851_2.png) [@cdelv](https://discourse.julialang.org/u/cdelv)\
**Post date:** [December 7, 2022, 1:56am UTC](https://discourse.julialang.org/t/is-there-a-symmetric-sparse-matrix-implementation-in-julia/91333/1 "2022-12-07T01:56:01Z")

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Hi, I want a symmetric sparse matrix that behaves like this

```julia
using StaticArrays
using Accessors
A = zeros(SHermitianCompact{3})
A = @set A[1,2] = 1
3×3 SHermitianCompact{3, Float64, 6} with indices SOneTo(3)×SOneTo(3):
 0.0 1.0 0.0
 1.0 0.0 0.0
 0.0 0.0 0.0

```

Basically, whenever I modify the value of the matrix I would want it to understand that it’s symmetric. Also, note that

```julia
A[2,1]
1.0

```

`SHermitianCompact` is great, is exactly what I want but it has a problem. I need to do a huge matrix, for example, 10\_000 x 10\_000. For every step, I will make a for loop that looks like this

```julia
for element in elements
    if condition(element)
        i,j = index(element)
        A = @set A[i,j] = 0.0
    else
       A = @set A[i,j] = value(element)
    end
end

```

I know for a fact that most of the matrix elements will be 0. Then, a sparse matrix will be Ideal. However looking through most of the space matrix implementations like `SparseMatricesCSR`, `SparseArrays`, `SuiteSparseGraphBLAS`, `SparseArrayKit`, and `SparseArrayKit` don’t have what I need. Actually, `SparseMatricesCSR` has a symmetric sparse but because of the lack of documentation, I couldn’t make it work.

At last, most of these implementations add 0 as a new element when

```julia
using ExtendableSparse
A = ExtendableSparseMatrix(zeros(4,4))
A[1,2] = 1.0
A[1,2] = 0.0
A
4×4 ExtendableSparseMatrix{Float64, Int64} with 1 stored entry:
  ⋅ 0.0 ⋅ ⋅ 
  ⋅ ⋅ ⋅ ⋅ 
  ⋅ ⋅ ⋅ ⋅ 
  ⋅ ⋅ ⋅ ⋅ 

```

and to remove it one has to call drop zeros. I would like it to do so automatically, I don’t want to have to call the function each time I add a zero.

Do you know of one package that has this implementation? Do you know a way of doing this in a good way? What do you recommend?

Thanks.

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<div class="post-metadata">

**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:** [December 7, 2022, 2:22am UTC](https://discourse.julialang.org/t/is-there-a-symmetric-sparse-matrix-implementation-in-julia/91333/2 "2022-12-07T02:22:09Z")

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You can create the upper (or lower) half and then use the [`Symmetric`](https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#LinearAlgebra.Symmetric) wrapper view from `LinearAlgebra`, or adding the transpose.

Whether using this method, or any other “symmetric method”, is a good idea ultimately depends on what you will use the matrix for. For example, if you are solving a linear system, the solver might not be faster and/or have special method for the symmetric case: the default Cholesky factorization will utilize the symmetry if you use the method I mentioned above, but there is nothing similar for the default LU factorization. For iterative methods I think it will be faster to have the full matrix too when doing the matrix-vector multiplications. Quite often it is much better to create the full matrix – the storage savings would only be a factor of 2 anyway.

> [@cdelv](#):
>
> I would like it to do so automatically, I don’t want to have to call the function each time I add a zero.

Adding new structural elements like that (and removing them) is pretty expensive, so I would not insert elements like this in the first place.

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<div class="post-metadata">

**Author:** ![cdelv](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cdelv/32/44851_2.png) [@cdelv](https://discourse.julialang.org/u/cdelv)\
**Post date:** [December 7, 2022, 2:28am UTC](https://discourse.julialang.org/t/is-there-a-symmetric-sparse-matrix-implementation-in-julia/91333/3 "2022-12-07T02:28:31Z")

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Thanks for your answer. Actually, I’m only using it to store and get data from the matrix. I’m not doing any linear algebra on it.