Testing the Generalized Nonsymmetric Eigenvalue Condition Estimation Routines

The main routines tested are xTGEXC, xTGSYL, xTGSNA, and xTGSEN. xTGEXC reorders the generalized Schur decomposition of a matrix pair, xTGSYL solves the generalized Sylvester equation 276#276, 277#277 for 74#74 and 140#140 given 278#278, 279#279, and 280#280, xTGSNA computes condition numbers for individual eigenvalues and eigenvectors of a matrix pair, and xTGSEN computes condition numbers for the average of a cluster of eigenvalues, as well as their corresponding right invariant subspace. Several auxiliary routines xGETC2, xGESC2, xTGDIF, xTGEX2, and xTGSY2 exist.

NOTE: There are known testing failures in condition number estimation routines in the generalized nonsymmetric eigenproblem testing. Specifically in sgd.out, dgd.out, cgd.out and zgd.out. The cause for the failures of some test cases is that the mathematical algorithm used for estimating the condition numbers could over- or under-estimate the true values in a certain factor in some rare cases.

For more details on eigencondition estimation, see LAPACK Working Note 87.