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[Lapack] Bug in LAPACK 3.2 dlarfb.f and likes

Hello Michael,

Thanks a lot for the bug report. We have reproduced all your sayings:  
your test code flags an error for NX from 0, 1, 2, up to N more or  
less, your fix to DLARFB fixes the problem. We observe this for  
lapack-3.2.1 and for our lapack in svn.

We need a little a bit of time to get through the code and understand  
the fix. One thing that bothers us is that DCKKQR did not catch the  
problem. (Note: we do text for various NB and NX in our test suite  
through setting the value with XLAENV and then using a fake ILAENV).

So, all this to say, that we will come back to your shortly on this one.

Best wishes,
Julie and Julien
On Jul 21, 2009, at 9:28 AM, Chuvelev, Michael wrote:

Hello,

I've found a bug in dlarfb.f recently, it can be revealed by dorgql  
blocked algorithm, for instance. I suspect the ordinal tests don't  
catch it because too high crosspoint is set in ilaenv.f NX=128. To  
catch the bug:
1) set less crosspoint in line 462 of ilaenv.f, for instance, NX=0
2) compile the testcase attached,
3) use the input data attached
You will have non-orthogonal vectors on the output.


dlarfb.f has been changed to reduce the number of reflectors needed  
to be applied, but it turns out sometimes we miss the last reflector  
to be applied. The newly introduced function iladlr detects last non- 
zero row, but in dlarfb we don't pay attention to the fact that the  
elementary reflectors

v v v
v v v
v v v
1 v v
  1 v
    1

could be kept along with a zero diagonal:

v v v
v v v
v v v
0 v v
  0 v
    0

which in fact reduce the number of reflectors to be applied, that is  
we miss the last one. I find the following logic appropriate in this  
case: substituting line 260 in dlarfb.f

               LASTV = MAX( K, ILADLR( M, K, V, LDV ) )

by the line

<                LASTV = MAX( K, ILADLC( M, K, V, LDV ) )+M-K

The original LASTV initialization is wrong.


Best regards,

Michael.


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Julie Langou; Research Associate in Computer Science
Innovative Computing Laboratory;
University of Tennessee from Denver, Colorado ;-)
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