The four driver routines have slightly different tests applied to them.

- For SGGES the following tests are computed:

263#263

where 264#264 and 265#265 are the 2 181#181 2 diagonal blocks of 250#250 and 85#85 corresponding to the 266#266th and 267#267th eigenvalues. - For SGGESX the following tests are computed:

268#268

where 264#264 and 265#265 are the 2 181#181 2 diagonal blocks of 250#250 and 85#85 corresponding to the 266#266th and 267#267th eigenvalues.

269#269

The test 160#160 is for precomputed test problems.`DIFtru`is the true value of DIF obtained by computing the minimum singular value of the matrix generated in solving the generalized Sylvester equation and`DIFest`is the estimated value of DIF obtained from`xTGSEN`, and where`PLtru`is the true value of PL obtained by computing the norm of the matrix L resulting from the solution of the generalized Sylvester equation and`PLest`is the estimated value of PL obtained from`xTGSEN`.

Test 8 is compared to 10*`THRESH`instead of`THRESH`.

Test 9 is a check for very ill-conditioned problems. It is possible with ill-conditioned problems for reordering to be (nearly) impossible which corresponds to very large condition numbers. So if reordering fails, it is checked that the true reciprocal condition number`DIFtru`is small (i.e. the condition is large) and it is checked that the estimated reciprocal condition number`DIFest`is zero (when reordering fails, the subroutine is supposed to return`DIFest`= 0).These test ratios are compared to the input parameter

`THRESH`. If a ratio exceeds`THRESH`, a message is printed specifying the test matrix, the ratio that failed and its value, just like the tests performed on the nonsymmetric eigenvalue problem computational routines.

- For SGGEV the following tests are computed:

270#270

where 151#151 are eigenvalues 271#271. All norms are 261#261. The scalings in the test ratios assure that the ratios will be 124#124, independent of 262#262 and 203#203, and nearly independent of 4#4. - For SGGEVX the following tests are computed:

272#272

where`Stru`273#273 is the exact reciprocal condition number for eigenvalue 274#274 and`Sest`273#273 is the estimated reciprocal condition number computed by`xTGSNA`, and`DIFtru`273#273 is the exact reciprocal condition number for eigenvector 274#274 and`DIFest`273#273 is the estimated reciprocal condition number computed by`xTGSNA`.

Test 4 is compared to 10*`THRESH`instead of`THRESH`.

All norms are 261#261. The scalings in the test ratios assure that the ratios will be 124#124, independent of 262#262 and 203#203, and nearly independent of 4#4.