Since the SVD decomposition is not unique (pairs of left and right singular vectors can have their sign flipped simultaneously), I was wondering to what extent the U and V matrix returned by scipy.linalg.svd() are 'deterministic' / always the same?
I tried it a few times with a random array on my machine and it seems to always return the same thing (fortunately), but could that vary across machines?
SciPy and Numpy both compute the SVD by out-sourcing to the LAPACK _gesdd routine. Any deterministic implementation of this routine will produce the same results every time on a given machine with a given LAPACK implementation, but as far as I know there is no guarantee that different LAPACK implementations (i.e. NETLIB vs MKL, OSX vs Windows, etc.) will use the same convention. If your application depends on some convention for resolving the sign ambiguity, it would be safest to ensure it yourself in some sort of post-processing of the singular vectors; one useful approach is given in Resolving the Sign Ambiguity in the
Singular Value Decomposition (pdf)
