The four drivers have slightly different tests applied to them.

xGEEV takes the input matrix 16#16 and computes a matrix of its right eigenvectors 149#149, a matrix of its left eigenvectors 150#150, and a (block) diagonal matrix 151#151 of eigenvalues. If 151#151 is real it may have 2 by 2 diagonal blocks corresponding to complex conjugate eigenvalues. The test ratios computed are:

152#152

153#153, 154#154 and 155#155 check whether 151#151 or 149#149 or 150#150 is computed identically independent of whether other quantities are computed or not. 156#156 and 157#157 also check that the component of 149#149 or 150#150 of largest absolute value is real.

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.

In addition to the above tests, xGEEVX is tested by computing the test ratios 147#147 through 158#158. 147#147 tests whether the output quantities SCALE, ILO, IHI, and ABNRM are identical independent of which other output quantities are computed. 159#159 tests whether the output quantity RCONDV is independent of the other outputs. 160#160 and 158#158 are only applied to the matrices in the precomputed examples:

161#161

RCONDV (RCONDE) is the array of output reciprocal condition numbers of eigenvectors (eigenvalues), RCDVIN (RCDEIN) is the array of precomputed reciprocal condition numbers, and 162#162 ( 163#163) is the condition number of RCONDV (RCONDE).

xGEES takes the input matrix 16#16 and computes its Schur decomposition 164#164 where 165#165 is orthogonal and 85#85 is (quasi) upper triangular, optionally sorts the eigenvalues on the diagonal of 85#85, and computes a vector of eigenvalues 151#151. The following test ratios are computed without sorting eigenvalues in 85#85, and compared to THRESH:

166#166

155#155 through 167#167 are the same test ratios but with sorting the eigenvalues . 168#168 indicates whether the sorting was done successfully.

In addition to the above tests, xGEESX is tested via ratios 169#169 through 170#170. 169#169 (171#171) tests if RCONDE (RCONDV) is the same no matter what other quantities are computed. 172#172 and 170#170 are only applied to the matrices in the precomputed examples:

173#173

RCONDV (RCONDE) is the output reciprocal condition number of the selected invariant subspace (eigenvalue cluster), RCDVIN (RCDEIN) is the precomputed reciprocal condition number, and 162#162 ( 163#163) is the condition number of RCONDV (RCONDE).