Generalized eigenvalues with GUPTRI

[Markus Wageringel]

Hello everyone.

In Sage 9.2.beta11, Sage's functionality for eigenvalues and eigenvectors has been extended in two directions:

• In #30393, Marc Mezzarobba has added wrappers for arb's new support for arbitrary precision computation of eigenvalues and eigenvectors.

• In #29243, support for computing generalized eigenvalues via SciPy was added (both reviewed by Sébastien Labbé – thanks).

Adding to the second point, I would like to share an external package, guptri_py [1], that I created for NumPy and Sage. It is a small wrapper for the Fortran library GUPTRI [2] and can be used to compute generalized eigenvalues when a matrix pencil is singular.

To give some details, for two matrices A and B, the roots of the polynomial det(A - λB) are called generalized eigenvalues. If the polynomial is constantly zero, the pencil is said to be singular, in which case eigenvalues are more difficult to define and to compute – this is what GUPTRI can be used for (in contrast to SciPy/LAPACK).

I hope this package might be useful for someone.

By the way, is there a place that lists external Sage packages to make them easier to find? All I could find is a collection of old SPKGs.

Best regards,

Markus

[1] https://github.com/mwageringel/guptri_py

[2] https://www8.cs.umu.se/research/nla/singular_pairs/guptri/

[Matthias Koeppe]

On Sunday, September 6, 2020 at 7:46:18 AM UTC-7, Markus Wageringel wrote:

Hello everyone.

In Sage 9.2.beta11, Sage's functionality for eigenvalues and eigenvectors has been extended in two directions:

• In #30393, Marc Mezzarobba has added wrappers for arb's new support for arbitrary precision computation of eigenvalues and eigenvectors.

• In #29243, support for computing generalized eigenvalues via SciPy was added (both reviewed by Sébastien Labbé – thanks).

Could you add a bit to https://wiki.sagemath.org/ReleaseTours/sage-9.2#Linear_and_multilinear_algebra please?

 

Adding to the second point, I would like to share an external package, guptri_py [1], that I created for NumPy and Sage. It is a small wrapper for the Fortran library GUPTRI [2] and can be used to compute generalized eigenvalues when a matrix pencil is singular.[...] 

By the way, is there a place that lists external Sage packages to make them easier to find? All I could find is a collection of old SPKGs.

https://wiki.sagemath.org/SageMathExternalPackages

 

[Markus Wageringel]

Thank you for the link. I am a bit surprised I did not find that myself.

I have been planning to add something to the release notes and will do so soon. I do not have a legacy trac account yet, but I have just sent a request for one.