Hi,
A user of statistical software R (cran.rproject.org) reported a problem when
trying to get an eigen decomposition of a particular symmetric matrix. The
problem can be tracked down to lapack routine dsyevr failing to return.
Specifically, routine DLARRB gets stuck in an infinite loop: the reason for
this is that while refining eigenvalues this routine compares an error bound
on an eigenvalue to the difference between two other eigenvalues 
unfortunately this difference has become negative, so the convergence
condition is never met. (The matrix does have high proportion of repeated and
zero eigenvalues, but it's not a problem to decompose it using other lapack
routines.)
Several R developers have replicated the problem (using R, which calls lapack)
on a variety of platforms (on one machine we got convergence), but we are at
a loss about how to fix it, and are unable to find any reference to such a
problem by internet searching. I have therefore replicated the problem using
a small fortran wrapper program, which loads the offending matrix, and calls
lapack directly.
I used lapack 3 from netlib, with the source patches from
www.netlib.org/lapack/patch
and the blas supplied with lapack. The test suites indicate no problems. I am
running suse linux 9.3 on a pentium xeon machine, and g77 (gcc 3.3.5). I've
tried turning off all optimization when building the blas, lapack and the
test program, but the problem persists.
I've attached the wrapper program, lap.f (please excuse my fortran) and the
problematic matrix dumped as binary, thematrix.bin, to be read by lap.f.
Any help would be much appreciated!
best,
Simon

Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2 7AY UK
+44 1225 386603 www.maths.bath.ac.uk/~sw283
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