pinv bug: matrix misdiagnosed as diagonal

[PetrKryslUCSD]

The code

A = [1.0 0.0;0.0 1.0;0.0 0.0]
A1 = pinv(A):

produces

[1.0 0.0 1.0;0.0 0.0 0.0]

An incorrect answer, which is due to the identification of A as diagonal on line
https://github.com/JuliaLang/julia/blob/bf534986350a991e4a1b29126de0342ffd76205e/stdlib/LinearAlgebra/src/dense.jl#L1433

I think the solution could be to check that the matrix is square and isdiag returns true.

Or, perhaps isdiag does not work correctly, and the solution is to fix that function to identify matrix as diagonal only if it is square?

The svd code below the if block would have worked correctly.
https://discourse.julialang.org/t/bug-in-linearalgebra-pinv/76663/2

[martinholters]

I think the problem is the indexing operation in
https://github.com/JuliaLang/julia/blob/bf534986350a991e4a1b29126de0342ffd76205e/stdlib/LinearAlgebra/src/dense.jl#L1439
Using PermutedDimsArray(B, (2,1))[ind] on the LHS might do the trick.
EDIT: On second thought, B[diagind(B)] should work just as well and is a bit simpler.

[PetrKryslUCSD]

That might work.

[hyrodium]

Note that this bug doesn't exist on Julia v1.6.6.

v1.6.6

julia> A = [1.0 0.0;0.0 1.0;0.0 0.0]
3×2 Matrix{Float64}:
 1.0  0.0
 0.0  1.0
 0.0  0.0

julia> A1 = pinv(A)
2×3 Matrix{Float64}:
 1.0  0.0  0.0
 0.0  1.0  0.0

v1.7.2

julia> A = [1.0 0.0;0.0 1.0;0.0 0.0]
3×2 Matrix{Float64}:
 1.0  0.0
 0.0  1.0
 0.0  0.0

julia> A1 = pinv(A)
2×3 Matrix{Float64}:
 1.0  0.0  1.0
 0.0  0.0  0.0

Maybe JuliaLang/julia#39756 is related?