Example (from Program LA_GGEVX_EXAMPLE)

The results below are computed with $\epsilon = 1.19209 \times 10^{-7}$.

$$A = \left( \begin{array}{rrrrr} -2 - 9i & 1 + 2i & -6 +2i & ... ... - 8i & 5 + 10i & -4 + 2i & 1 -i & -4 + 0i \end{array} \right)$$

$$B = \left( \begin{array}{rrrrr} -7 + 5i & 4 + 12i & 5 + ... ... -2 - 2i & -10 - 3i & 4 + 3i & -3 -i \end{array} \right)$$

Arrays A and B on entry:

$$\begin{array}{c} {\bf A} \\ \begin{array}{\vert rrrrr\vert}... ...& (-4, 2) & (1, -1)& (-4, 0) \\ \hline \end{array} \end{array}$$

$$\begin{array}{c} {\bf B} \\ \begin{array}{\vert rrrrr\vert}... ...(-10, -3) & (4, 3)& (-3, -1) \\ \hline \end{array} \end{array}$$

The call:

   CALL LA_GGEVX( A, B, ALPHA, BETA, BALANC='B', LSCALE=LSCALE, & 


RSCALE=RSCALE, ABNRM=ABNRM, & 


BBNRM=BBNRM, RCONDE=RCONDE, & 


RCONDV=RCONDV ) 

${\bf LSCALE, RSCALE, ABNRM, BBNRM, RCONDE, RCONDV, ALPHA, BETA}$ and LAMBDA on exit:

$$\hspace{-0.50 cm} \begin{array}{cc} {\bf LSCALE} \\ \begin{... ...1.00000 & 1.00000 & 1.00000 \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf ABNRM} = 2.76734 \times 10^{1} \hspace{1.00 cm} {\bf BBNRM} = 3.61864 \times 10^{1} \end{array}$$

$$\hspace{-0.50 cm} \begin{array}{cc} {\bf RCONDE} \\ \begin{... ... 2.67197 & 1.45866 & 1.61397\\ \hline \end{array} \end{array}$$

$$\hspace{-0.50 cm} \begin{array}{cc} {\bf ALPHA} \\ \begin{a... ....000, 0.000)& (-1.509,2.026) \\ \hline \end{array} \end{array}$$

$$\hspace{-0.50 cm} \begin{array}{cc} {\bf BETA} \\ \begin{ar... ...3.794,0.000)& (17.099,0.000) \\ \hline \end{array} \end{array}$$

$$\hspace{-0.50 cm} \begin{array}{cc} {\bf LAMBDA} \\ \begin{... ...0.000,0.000)& (-0.088,0.119) \\ \hline \end{array} \end{array}$$

Balancing was not needed.

The $l_{1}$ norm of $A$ is $2.76734 \times 10^{1}$ and the $l_{1}$ norm of $B$ is $3.61864 \times 10^{1}$.

The reciprocal condition numbers of the eigenvalues are:

$$\left( \begin{array}{lllll} 2.12830 & 1.84798 & 8.09452 & 5.56294 & 4.77657 \end{array} \right)$$

The reciprocal condition numbers of the eigenvectors are:

$$\left( \begin{array}{lllll} 2.29658 & 1.83061 & 2.67197 & 1.45866 & 1.61397 \end{array} \right)$$