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[Lapack] Scaling in xSTEQR, xSTERF

Dear LAPACKers:

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.

Thanks.
Pat.
 
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