On Tue, May 3, 2022 at 8:40 PM Leo Fang <leo80...@gmail.com> wrote: > Hi, I am catching up with an assigned task that I slipped. I am wondering > a few things about the numpy.linalg.eig() API (eigvals() is also included > in this discussion, but for simplicity let's focus on eig()). AFAIU the > purpose of eig() is for handling general eigen-systems which have left and > right eigenvectors (that could differ beyond transpose/conjugate).
For this, I have two questions: > > 1. What's the history of NumPy adding this eig() routine? My guess would > be NumPy added it because Matlab had it, but I couldn't tell from a quick > commit search. > It essentially dates back to Numeric, though the name was a bit different. But the core feature of only computing right-eigenvectors was there. scipy.linalg.eig() came along and expose both left- and right-eigenvalues (with close to the present signature, I think). Then numpy took over from Numeric and adopted the scipy.linalg names for the routines, but cut out a number of the features that made some of the interfaces complicated. Since Numeric only did right-eigenvalues (what most people want, even in the general-matrix case), so did numpy. > 2. Would it be possible to deprecate/remove this API? From past > discussions with users and developers, I found: > - numpy.linalg.eig() only returns the right eigenvectors, so it's not very > useful: > * When the left eigenvectors are not needed --- which is the majority of > the use cases --- eigh() is the right routine, but most users (especially > those transitioning from Matlab) don't know it's there > eigh() is only for symmetric/Hermitian matrices. > * When the left eigenvectors are needed, users have to use > scipy.linalg.eig() anyway > It seems to me that you are assuming that in the non-Hermitian case, the right-eigenvectors are useless without the left-eigenvectors. It isn't obvious to me why that would be the case. It is true that the left- and right-eigenvectors differ from each other, but it's not clear to me that in every application with a general matrix I need to compute both. - A general support for eig() could be challenging (numerical issues), and > doing SVDs instead is usually the better way out (in terms of both > numerical stability and mathematical sense). > Computing the left-eigenvectors is no real problem. The underlying _GEEV LAPACK routine can do it if asked. It's the same routine under scipy.linalg.eig(). -- Robert Kern
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