`checksquare` necessary for `inv(::SVD)`?

[ggebbie]

checksquare on SVD Factorization failing, as I have a case with the SVD of a non-square matrix. Worked on Julia 1.11. Fails 1.12. Change in behavior tracked to this commit/diff.

67c1103#diff-cdde201629acbae390e807c356181577a7cb018f3b79cfbcac02ae8556ec0cd5L315

[ViralBShah]

That commit looks like it was @stevengj

[ggebbie]

You're right, Viral. Makes me second guess whether I'm misunderstanding something! But it should be ok to make an SVD Factorization with a rectangular matrix and then use inv to make a generalized (but not true) inverse. Maybe the issue is that inv should be reserved for true inverses.

Perhaps (\) (matrix left divide) is better than inv for what I'm trying to do.

[dkarrasch]

The rationale was to reserve inv for inverses (and make it consistent with inv(::Matrix) and introduce pinv for what you're doing.

[ggebbie]

Thanks a lot! Makes sense. Will close. Thanks, Daniel and Viral.

[ggebbie]

If I understand correctly, the pinv solution is proposed but does not yet appear to be implemented.

julia> pinv(F)
ERROR: MethodError: no method matching pinv(::SVD{Float64, Float64, Matrix{Float64}, Vector{Float64}})
The function `pinv` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  pinv(::Diagonal{T, V} where V<:AbstractVector{T}, ::Real) where T
   @ LinearAlgebra ~/.julia/juliaup/julia-1.12.1+0.x64.linux.gnu/share/julia/stdlib/v1.12/LinearAlgebra/src/diagonal.jl:911
  pinv(::Diagonal{T, V} where V<:AbstractVector{T}) where T
   @ LinearAlgebra ~/.julia/juliaup/julia-1.12.1+0.x64.linux.gnu/share/julia/stdlib/v1.12/LinearAlgebra/src/diagonal.jl:896
  pinv(::Transpose{T, <:AbstractVector} where T)
   @ LinearAlgebra ~/.julia/juliaup/julia-1.12.1+0.x64.linux.gnu/share/julia/stdlib/v1.12/LinearAlgebra/src/adjtrans.jl:518
  ...

Stacktrace:
 [1] top-level scope
   @ REPL[14]:1

[dkarrasch]

It is (or should be). It's right above your quoted code snippet.

[dkarrasch]

Ah, maybe we backported the checksquare change but not the "new feature" pinv(::SVD)?

[ggebbie]

That's what it looks like to me. I see pinv on GitHub, but it doesn't seem to exist in my Julia 1.12 installation. Thanks for looking into it.

[stevengj]

As noted in #1387, explicitly forming the pinv matrix (or the inv matrix) is not generally numerically stable — you are generally better off just keeping the SVD as a factorization object F and then applying the pseudoinverse with F \ …

That being said, if you really need to compute an explicit pinv matrix from an SVD object F on 1.12 you can do it explicitly by F.V * pinv(Diagonal(F.S)) * F.U'