1×1 matrix 0 appears positive definite and cholesky doesn't fail

[cecileane]

When an MMatrix or SMatrix is of dimension 1-by-1, it is detected as being positive definite even if its entry is 0, and its cholesky decomposition does not fail. Below I'm using StaticArrays v1.6.5 and julia v1.9.2.

julia> using LinearAlgebra, StaticArrays

julia> m = MArray{Tuple{1,1}}(0.0); # 1×1 MMatrix

julia> isposdef(m) # should be false
true

julia> isposdef(cholesky(m)) # also true: cholesky didn't fail
true

julia> cholesky(m).info # 0 so it's supposedly PosDef
0

same with an SMatrix:

julia> s = SArray{Tuple{1,1}}(0.0);

julia> isposdef(s)
true

julia> isposdef(cholesky(s)) # doesn't fail
true

Things are as expected if the 1×1 matrix has a negative entry, or it it's a regular matrix:

julia> isposdef(MArray{Tuple{1,1}}(-1.0))
false

julia> isposdef([0.0;;])
false

[bstkj]

I believe this bug is fixed by JuliaLang/julia@ee3b779 (basically, a generic cholesky method is being called that does not throw an error for positive semidefinite matrices), though this has not been incorporated as of the latest stable release (1.9.3).

[jishnub]

This package defines their own Cholesky implementation, which seems to still have this bug. The issue is fixed for general matrices, but not for StaticArrays.

[cecileane]

Yes, thank you for this. To confirm: the bug is still here using julia v0.10.0 and StaticArrays v1.9.1.