[SciPy-user] eigenvalue

Pearu Peterson pearu at scipy.org
Wed Dec 8 06:04:54 CST 2004



On Wed, 8 Dec 2004, Tiziano Zito wrote:

> On Wed 08 Dec, 05:31, Pearu Peterson wrote:
>>
>> The state of including symeig to scipy is the following: lib.lapack
>> contains all wrappers in symeig except for sygvx,hegvx lapack routines
>> (that enable to compute only a range of eigenvalues of generalized
>> eigenvalue problem).
>> When these get wrapped, I'll patch scipy.eig so that
>> it'll use more efficient lapack routines to solve eigenvalue problems of
>> symmetric/hermitian matrices. However, one can use lib.lapack routines
>> already to solve eigenproblems as quick as symeig.
>
> How do you plan to patch scipy.linalg.eig?  I suppose you are going
> to add a switch keyword argument.

Yes. And may be also provide scipy.linalg.symeig function.

>  If otherwise you plan to automatically check if the matrices are 
> symmetric (hermitian),

No. That will be left to the user to check. I'll assume that users will 
know what they are doing when using scipy.linalg.symeig, for instance.

> note that the generalized symmetric eigenvalue problem Az=lBz requires B 
> to be not only symmetric (hermitian) but also positive definite (see for 
> example: http://www.netlib.org/lapack/lug/node34.html ). To check for 
> positive definitiveness however would require the solution of another 
> eigenvalue problem :))

Right. Again, it's up to the user to feed correct data to 
scipy.linalg.symeig. It's too expensive to assume that users
may want to abuse scipy.linalg.symeig:)

Thanks for your notes,
Pearu



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