generalized eigensystems

[Patrick Alken <patrick dot alken at colorado dot edu>]

Hello all,

  The current CVS contains support for generalized eigensystems.
All the functions are documented in eigen.texi. I have tested
the code for randomized and integer matrix systems up to N = 1000
and compared to lapack and things look good. All my development/testing
was done on amd32/linux so if anyone is willing to test it out on
other archs I'd appreciate it. There is a test program in
eigen/testgen.c which will generate matrices, compute eigenvalues,
and test them against lapack's output. The header of testgen.c
explains how to compile it. Once its compiled, you can just do:

./testgen -n 100 -z

to test N = 100 matrices and compute the schur vectors and test them
too. Sometimes it will output a small discrepancy with lapack
(say around a 10^{-5} difference for an eigenvalue) and most of
these I have tracked down to an initial near-singular or ill-conditioned
matrix input in which case lapack's output can't be trusted either.
But you can send along any output from the test program to me and
I'll have a look at it.

Thanks,
Patrick Alken