IBM and HP specific : Sign of eigenvector in DSYGV

From: Arindam Chakraborty (arimail77_at_yahoo.com)
Date: 03/27/04 

Date: 27 Mar 2004 00:33:11 -0800

I am solving a generalized eigenvalue equation :
          A x = lambda B x
where A is symmetric and B is positive defined and symmetric, x is the
eigenvector with eigenvalue lambda.

I am using DSYGV routine from ESSL (version 3.3) on IBM SP.
On HP(HP Server RX2600 nodes) I use the same routine (DSYGV)
from LAPACK.

To test the routines on the different machines, the test matrix from
ESSL
doc pages was used :
  http://hpcf.nersc.gov/vendor_docs/ibm/essl/essl195.html#HDRHSSYGV
 EXAMPLE : 2
----------------------------------------------------------------
Test matrices stored in lower packed mode
----------------------------------------------------------------
        * *
        | -1.0 . . |
A = | 1.0 1.0 . |
        | -1.0 -1.0 1.0 |
        * *

        * *
        | 2.0 . . |
B = | 1.0 2.0 . |
        | 0.0 1.0 2.0 |
        * *
-------------------------------------------------------------------
One of the eigenvectors from the calculation of HP
had an sign difference from the ESSL results.

(The results from the ESSL calculation can be found here :
 http://hpcf.nersc.gov/vendor_docs/ibm/essl/essl195.html#HDRHSSYGV )

Since eigenvectors are arbitrary to with a sign difference....I was
wondering
if LAPACK (or LAPACK in HP ?) and ESSL follow different sign
conventions for
eigenvectors.

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