[SciPy-user] eigenvalue

Nils Wagner nwagner at mecha.uni-stuttgart.de
Wed Dec 8 06:00:58 CST 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.  If otherwise you plan to
>automatically check if the matrices are symmetric (hermitian),  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 :))

This is not correct. You may use a Cholesky decomposition of the matrix 
B, i.e

B = C \diag{d_i} C^\top

B is spd if all entries d_j > 0.


>Thank you and greetings,
>Tiziano and Pietro
>SciPy-user mailing list
>SciPy-user at scipy.net


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