Likely bug in `issymmetric(A::AbstractSparseMatrixCSC)`

[sztal]

I found a likely bug in issymmetric(A::AbstractSparseMatrixCSC), which considers symmetric a matrix which is clearly non-symmetric. Here is an example.

using LinearAlgebra, SparseArrays
S = sparse([2, 3, 1], [1, 1, 3], [1, 1, 1], 3, 3)

S looks like this:

3×3 SparseMatrixCSC{Int64, Int64} with 3 stored entries:
 ⋅  ⋅  1
 1  ⋅  ⋅
 1  ⋅  ⋅

And this is what issymmetric does:

M = Matrix(S)
issymmetric(S)  # true
issymmetric(M)  # false

The bug most likely applies also to ishermitian.

Version info

Julia Version 1.11.3
Commit d63adeda50d (2025-01-21 19:42 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 16 × AMD Ryzen 9 5900HX with Radeon Graphics
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 16 virtual cores)
Environment:
  JULIA_PROJECT = @.
  JULIA_PKG_PRESERVE_TIERED_INSTALLED = true
  JULIA_REVISE = manual
  JULIA_EDITOR = vim

Pkg status

⌃ [4c555306] ArrayLayouts v1.11.0
  [6e4b80f9] BenchmarkTools v1.6.0
  [31a5f54b] Debugger v0.7.10
  [31c24e10] Distributions v0.25.117
  [1a297f60] FillArrays v1.13.0
  [86223c79] Graphs v1.12.0
⌃ [aa1ae85d] JuliaInterpreter v0.9.41
⌃ [0b1a1467] KrylovKit v0.9.3
⌃ [5078a376] LazyArrays v2.4.0
  [295af30f] Revise v3.7.2
  [2913bbd2] StatsBase v0.34.4
Info Packages marked with ⌃ have new versions available and may be upgradable.

[jishnub]

Could you look into which method is used for the check?

[sztal]

Sure!

@which issymetric(S)
# @ SparseArrays ~/.julia/juliaup/julia-1.11.3+0.x64.linux.gnu/share/julia/stdlib/v1.11/SparseArrays/src/sparsematrix.jl:4034

More specifically, @edit issymmetric(S) takes me to:

## Structure query functions
issymmetric(A::AbstractSparseMatrixCSC) = is_hermsym(A, identity)