The Nonsymmetric Eigenvalue Drivers

The driver routines for the nonsymmetric eigenvalue problem are

xGEEV

eigenvalue/eigenvector driver,

xGEEVX

expert version of xGEEV (includes condition estimation),

xGEES

Schur form driver, and

xGEESX

expert version of xGEES (includes condition estimation).

For these subroutines, some tests are done by generating random matrices of a dimension and type chosen by the user, and computing error bounds similar to those used for the nonsymmetric eigenvalue computational routines. Other tests use a file of precomputed matrices and condition numbers, identical to that used for testing the nonsymmetric eigenvalue/vector condition estimation routines.

The parameters that can be varied in the random matrix tests are:

• the order 13#13 of the matrix 16#16
• the type of test matrix 16#16
• five numerical parameters: NB (the block size), NBMIN (minimum block size), NX (minimum dimension for blocking), NS (number of shifts in xHSEQR), and NBCOL (minimum column dimension for blocking).