On Tue, May 3, 2022 at 6:41 PM Leo Fang <leo80042@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. 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 for Hermitian matrices, the svd won't return eigenvectors in the general case, especially when they are not orthogonal or form a complete basis. The left eigenvectors can be obtained by passing the transpose to eig(). In my experience, the main problem with eig() is accuracy, and sometimes (IIRC) it doesn't find all the eigenvectors, so it should not be used when the matrix is Hermitian.
* When the left eigenvectors are needed, users have to use scipy.linalg.eig() anyway - 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).
Chuck