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[Lapack] matrix splitting problem with dstebz and sstebz


Hello Phil,

Thanks for the bug report. I have added your bug report to the LAPACK 
Errata file. See: http://www.netlib.org/lapack/Errata/ , bug0032. We will 
try to have a look at some points.

Best wishes,
Julien

On Mon, 29 Jun 2009, Phil DeMier wrote:


Greetings,

We have discovered a problem with DSYEVX. The problem occurs for certain 
matrices created using a specific algorithm.

We are able to work around the problem by removing the "matrix splitting" 
code in dstebz. This problem also occurs in sstebz.

DO 10 J = 2, N
TMP1 = E( J-1 )**2
!! IF( ABS( D( J )*D( J-1 ) )*ULP**2+SAFEMN.GT.TMP1 ) THEN
!! ISPLIT( NSPLIT ) = J - 1
!! NSPLIT = NSPLIT + 1
!! WORK( J-1 ) = ZERO
!! ELSE
WORK( J-1 ) = TMP1
PIVMIN = MAX( PIVMIN, TMP1 )
!! END IF
10 CONTINUE

Please see the attached test program testevx.f which demonstrates the failure.
(See attached file: testevx.f)

Output from the test:


*** Math check results for DSYT22 with N= 7 and M= 5
*** exceeded the threshold value of .10000000D+03

*** Math check: | U' A U - S | / ( |A| m ulp )
*** result was .76390963D+13
*** Math check: | I - U'U | / ( m ulp )
*** result was .15278193D+15






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