Thanks for the bug report. I have added your bug report to the LAPACK
Errata file. See: http://www.netlib.org/lapack/Errata/ , bug0036. We will
try to have a look at some points.
On Fri, 24 Jul 2009, Pat Quillen wrote:
During the process of upgrading to LAPACK 3.2, we noticed that the routines
xSTEQR and xSTERF are calling xLANST to compute the infinity norm of the
input matrix, and using this value to scale. It seems that these routines
should probably use xLANST with first input 'M' and scale by the element with
maximum absolute value. This would be consistent with the driver routines
xSTEVy, as well as with the xSTEMR and xSTEDC routines. Changing the
appropriate calls to xLANST would probably also necessitate changing the
constants SSFMIN and SSFMAX. For example, one might replace the scaling
logic in xSTEQR to be similar to that found in xSTEV.
We were motivated to look at this as one of our tests for eigs began to fail
with the recent change to xLASCL to handle CFROM == Inf. eigs is based on
ARPACK, which ultimately calls xSTEQR. Our test executes eigs on the matrix
A = [0 realmax; realmax 0]
The Lanczos process produces a tridiagonal matrix whose infinity norm
overflows, and for which the current version of DSTEQR will produce NaNs. By
replacing the scaling logic as outlined above, DSTEQR will produce the
eigenvalues +/-realmax. Of course, there will be matrices for which +/-Inf
are returned (use a different starting vector in Lanczos), but that is more
acceptable than NaN.
I have attached a copy of dsteqr.f with a proposed change, and I'd appreciate
any feedback you have.