[SciPy-user] Eigenvalues and eigenvectors

[Johannes Loehnert]

Hi,
>
> And it's only applicable to standard eigenvalue problems
> A x = \lambda x.
>
> How about generalized eigenvalue problems
> A x = \lambda B x with B spd (symmetric positive definite) ?

Well, having a quick look into the lapack docs, I found the following 
routines:

file dsygvx.f  dsygvx.f plus dependencies
prec double
for  Computes selected eigenvalues, and optionally, the eigenvectors of
,    a generalized symmetric-definite generalized eigenproblem,
,    Ax= lambda Bx,  ABx= lambda x,  or BAx= lambda x.
gams d4b1

file dspevx.f  dspevx.f plus dependencies
prec double
for  Computes selected eigenvalues and eigenvectors of a
,    symmetric matrix in packed storage.
gams d4a1

file dspgvx.f  dspgvx.f plus dependencies
prec double
for  Computes selected eigenvalues, and optionally, eigenvectors of
,    a generalized symmetric-definite generalized eigenproblem,  Ax= lambda
,    Bx,  ABx= lambda x,  or BAx= lambda x, where A and B are in packed
,    storage.
gams d4b1

(I presume there are corresponding complex versions, too.) However, these are 
not included in scipy right now.

Johannes