Dear Pat,
Thank you for pointing out this behaviour. Although I was not involved
in writing this routine, I don't imagine that this behaviour was
intended. I shall try to take a look at xLARFP in the next few days and
see if I can suggest anything to improve this.
As I am sure that you realise, xLARFP was written to produce a
non-negative BETA, so that in a factorization such as the QR, R would
have non-negative diagonals. (Although I notice that the comments in
xGEQRF and xGEQR2 do not actually say that the diagonals are real and
non-negative.)
Best wishes,
Sven.
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