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Testing the Eigenproblem Balancing and Backward Transformation Routines

The balancing routine, xGEBAL, is tested. xGEBAL balances a matrix and isolates some of its eigenvalues. The backward transformation routine to be tested is xGEBAK. xGEBAK back transforms the computed right or left eigenvectors if the original matrix was preprocessed by balance subroutine xGEBAL.

No parameters can be varied for either of the routines tested; the data files contain precomputed test problems along with their precomputed solutions. The reason for this approach is threefold. First, there is no simple residual test ratio which can test correctness of a condition estimator. Second, no comparable code in another library exists to compare solutions. Third, the condition numbers we compute can themselves be quite ill-conditioned, so that we need the precomputed solution to verify that the computed result is within acceptable bounds.

The test program xeigtsts reads in the data from the data files sbal.in and sbak.in respectively (for the REAL code). If there are no errors, a single message saying that all the routines pass the tests will be printed. If any routine fails its tests, an error message is printed with the name of the failed routine along with the number of failures, the number of the example with the worst failure, and the test ratio of the worst failure.


next up previous contents
Next: Testing the Nonsymmetric Eigenvalue Up: More About Testing Previous: Input File for Testing   Contents
Susan Blackford 2001-08-13