I am using dggevx routine to solve an nonsymmetric gevp.
The condition numbers of the input matrices are not that bad. However, I am ending up with a large negative eigenvalue which should not be there( which means that one of the alpha coefficients returned is negative).
I also checked the results in MATLAB for the same matrices, results are even worse where it detects some imaginary pairs also which should not be the case due to the construction of the problem.(in addition to the negative eigenvalue).
Apart from the negative eigenvalue, the results returned from dggevx are completely correct.
Do you have any idea why I am facing this problem? I am still thinking this is a conditioning issue however could not really find a cure yet.