Posted by Paul J. Hinker on July 08, 1997 at 14:17:02:

I have a question regarding the LAPACK GGBAK tests. I am

tuning LAPACK for windows NT for pentium processors. I am

getting a large error in the ZGGBAK tests. TEST_LAPACK/EIG/*chkgk.f

reads initial values for general matrices A, B, VL and VR where VL and

VR contain left and right eigenvectors for A and B. Then calls are made

to *GGBAL and *GGBAK to balance the matrices and form new eigenvectors.

Then the matrices E and F are formed by the following procedure

where the ' indicates a transformed matrix.

E = VL' A VR'

F = VL A' VR

E and F are compared element by element to find the maximum differance

VMAX.

Then a final error ratio is computed with:

RMAX = VMAX / ( EPS*MAX( ANORM, BNORM ) )

I have a case in the double complex test where the following two

complex number are found in corresponding elements of E and F.

(-846451377432000.,-834064341200000.) , (-846451377432001.,-834064341200001.)

Both the real and imaginary components are identical out to fourteen digits.

The reported ratio is 0.796D+04.

VMAX = 0.250000000000000

EPS = 0.222044604925031D-015

MAX(ANORM, BNORM) = 0.141421356237310D+012

It appears to me that the 80-bit floating point arithmetic

on the Pentiums is causing this error in the 15th significant

digit. Unfortunately, I'm not conversant enough with

the eigenvalue routines to make a mathematical argument

as to why I think this is a rounding error. Has anyone

seen this and handled it already?

Thanks

Paul Hinker

- Re: LAPACK routine test for ZGGBAK
**Scott Betts***10:21:10 7/09/97*(1)- Re: LAPACK routine test for ZGGBAK
**Scott Betts***10:06:20 7/11/97*(0)

- Re: LAPACK routine test for ZGGBAK