Fix [CDSZ]QRT17.
This is a routine to test DGELS which solves solves full rank overdetermined ( linear least squares ) or underdetermined (minimum norm) linear systems.
The check is, as follows,
(1) If the system is consistent, (smallresidual,) we check that
|| A^T ( b – A * x ) || / (||A||*||b||*max(M,N,NRHS)*eps)
is small (say less than 30).
(2) If the system is not consistent, (large residual,) we check that
|| A^T ( b – A * x ) || / (||A||*|| b - A*x ||*max(M,N,NRHS)*eps)
is small (say less than 30).
DQRT17 was checking in the not consistent case (large residual) that
|| A^T ( b – A * x ) || / (||A||*||x||*max(M,N,NRHS)*eps)
is small. It is a mistake and we need to change the ||x|| by a ||r||.
This fix is consistent with what the documentation says and makes more sense.