Cannot add SymTridiagonal matrices based on sparse vectors

[eschnett]

This fails:

julia> using LinearAlgebra
julia> using SparseArrays
julia> A = SymTridiagonal(sparsevec(Int[1]), sparsevec(Int[]))
julia> A + A
ERROR: MethodError: no method matching SymTridiagonal(::SparseVector{Int64, Int64}, ::Vector{Int64})

I assume the problem is that SymTridiagonal matrices accidentally convert the internal representation of the off-diagonal elements to a dense vector.

I am using

julia> versioninfo()
Julia Version 1.9.0-DEV.1130
Commit c80316e125* (2022-08-15 13:05 UTC)
Platform Info:
  OS: macOS (x86_64-apple-darwin21.6.0)
  CPU: 16 × Intel(R) Core(TM) i9-9980HK CPU @ 2.40GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-14.0.5 (ORCJIT, skylake)
  Threads: 8 on 16 virtual cores

[jishnub]

This works on v1.7.3, but not on higher versions

julia> A + A
1×1 SymTridiagonal{Int64, SparseVector{Int64, Int64}}:
 2

julia> versioninfo()
Julia Version 1.7.3
Commit 742b9abb4d (2022-05-06 12:58 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
  CPU: 11th Gen Intel(R) Core(TM) i5-1135G7 @ 2.40GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-12.0.1 (ORCJIT, tigerlake)
Environment:
  JULIA_EDITOR = subl

[inkydragon]

• ✔️ 1.7.2 (2022-02-06)
• ✔️ 1.8.0-DEV.682 (2021-10-08) f2080d57c8
• ❌ 1.8.0-DEV.683 (2021-10-08) 146de38b40
  Fix edge cases in SymTridiagonal when ev has an extra element (+, -, iszero, isone, etc.) julia#42472 cc: @mcognetta
• ❌ 1.8.0-beta1 (2022-02-23)
• ❌ 1.8.0-rc4 (2022-08-08)

[mcognetta]

The issue is that adding @views of SparseArrays makes it dense.

https://github.com/JuliaLang/julia/blob/ec98087cbf19bac26f6be05df9282746b0cffe78/stdlib/LinearAlgebra/src/tridiag.jl#L207

https://github.com/JuliaLang/julia/blob/ec98087cbf19bac26f6be05df9282746b0cffe78/stdlib/LinearAlgebra/src/LinearAlgebra.jl#L449-L453

julia> z = @view sparse([1, 2, 3])[1:3]
3-element view(::SparseVector{Int64, Int64}, 1:3) with eltype Int64:
 1
 2
 3

julia> z + z
3-element Vector{Int64}:
 2
 4
 6

I will see what can be done quickly.

[mcognetta]

Ok I have a fix but I am not quite sure how to commit to SparseArrays now that it is its own package.

[jishnub]

Just open a PR on the SparseArrays repo?

[mcognetta]

I meant that a copy of SparseArrays still shows up in the Julia stdlib directory when opening it in VSCode, etc. but changes to it didn't get tracked by git.

Anyway: JuliaSparse/SparseArrays.jl#225

[inkydragon]

@mcognetta After the pr is merged, just ask someone to BumpStdlibs. like JuliaLang/julia#46266

[SobhanMP]

Is there any reason the diagonals of SymTridiagonal cannot have different types?

[mcognetta]

I think that it is possible, but that is a much bigger change than necessary to fix this (all structured matrix types would have to be updated, and Tridiagonal could have 3 different types. I haven't heard of much need for this, but that's not necessarily an end-all reason for not doing it).