The main routines tested are xTREXC, xTRSYL, xTRSNA and xTRSEN. xTREXC reorders eigenvalues on the diagonal of a matrix in Schur form, xTRSYL solves the Sylvester equation 275#275 for 98#98 given 16#16, 97#97 and 67#67, xTRSNA computes condition numbers for individual eigenvalues and right eigenvectors, and xTRSEN computes condition numbers for the average of a cluster of eigenvalues, as well as their corresponding right invariant subspace. Several auxiliary routines xLAEQU, xLAEXC, xLALN2, xLAQTR, and xLASY2 are also tested; these are only used with real (x=S or x=D) data.
No parameters can be varied; 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 file sec.in (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.
For more details on eigencondition estimation, see LAPACK Working Note 13 .