Is there a Symmetric Sparse Matrix Implementation in Julia?

General Usage
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1

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

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

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

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

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.

2

You can create the upper (or lower) half and then use the 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.

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

1 Like
3

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.