[SciPy-dev] integration of symeig in SciPy

[alex griffing]

Tiziano Zito wrote:
> Dear SciPy devs, 
>
> there has been some discussion about integrating symeig in SciPy.
> symeig <http://mdp-toolkit.sourceforge.net/symeig.html> is a Python
> wrapper for the LAPACK functions to solve the standard and
> generalized eigenvalue problems for symmetric (hermitian) positive
> definite matrices. It is superior to the scipy "linalg.eigh" wrapper
> because it wraps *all* relevant LAPACK routines, enabling for
> example to just return a subset of all egenvectors/eigenvalues,
> which is a killer feature if you are dealing with huge-nonsparse
> matrices. Some of these LAPACK routines are available in
> scipy.lib.lapack.flapack and can be accessed through
> scipy.lib.lapack.get_lapack_funcs . Some of them are still missing
> in scipy, while symeig offers a unified interface to all relevant
> LAPACK functions.  symeig has been dowloaded  more than 1300 times
> since its first public appearance on sourceforge (under the
> mdp-toolkit package) in 2004. It features a complete unit test and a
> telling doc-string. I am one of the authors of symeig and have been
> contacted by some scipy devs to discuss the integration of symeig in
> scipy. I am more than willing to help doing this. The most difficult
> part (the LGPL license) has been addressed already: I've re-issued
> symeig under a BSD license. Next step would be to adapt symeig code
> and tests to the scipy framework. Some questions to you:
>
> - where would you like to have symeig? (I would suggest scipy.linalg)
>
> - should we change the signature to match or resamble that of other
>   eigenproblem-related functions in scipy?
>
> - is there a responsible scipy dev for the linalg package I can bother
>   with any questions I may have in the process?
>
> - do I get svn commit rights or should I work on a local copy and
>   send a patch?
>
> let me know, 
>
> tiziano
>   

This sounds like it would be very useful for scipy although I am just a 
user not a dev.  Could I use symeig to extract only the eigenvector 
corresponding to the largest eigenvalue, given a non-sparse symmetric 
real matrix whose eigenvalues are all positive except for exactly one 
that is zero?  The documentation for symeig says that it works for 
"symmetric (hermitian) definite positive matrices" but I guess mine 
would be a "symmetric (hermitian) semi-definite positive matrix".  If 
symeig wouldn't work, is there another way I could do this without using 
eigh to get the full eigendecomposition?

Thanks,
Alex