Example 1 (from Program LA_GGES_EXAMPLE)

$$A = \left( \begin{array}{rrrrr} -2 & -1 & -8 & -1 & 1 \\ ... ... 1 & -2 & 0 & -2 \\ -2 & 0 & 2 & 1 & 2 \end{array} \right)$$

Arrays ${\bf A}$ and B on entry:

$$\begin{array}{c} {\bf A} \\ \begin{array}{\vert rrrrr\ver... ... -2 \\ -2 & 0 & 2 & 1 & 2 \\ \hline \end{array} \end{array}$$

The call:
CALL LA_GGES( A, B, ALPHAR, ALPHAI, BETA)

${\bf A, B, ALPHAR, ALPHAI}$ and BETA on exit:

$$\begin{array}{cc} {\bf A} \\ \begin{array}{\vert rrllr\ve... ...00000 & ~~0.00000 & -1.08703 \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf B} \\ \begin{array}{\vert rlllr\ve... ....00000 & ~~0.00000 & 2.48762 \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf ALPHAR} \\ \begin{array}{\vert rrr... ...70 \times 10^{-1} & -1.08703 \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf ALPHAI} \\ \begin{array}{\vert rrr... ...4.94864 & -1.20932 & 0.00000 \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf BETA} \\ \begin{array}{\vert rrrrr... ...810 \times 10^{-1} & 2.48762 \\ \hline \end{array} \end{array}$$

The block upper triangular matrix $S$ is:

$$S = \left( \begin{array}{rrllr} -1.98687 & 6.26806 & -5.95... ...0000 & ~~0.00000 & ~~0.00000 & -1.08703 \end{array} \right) .$$

The upper triangular matrix $T$ is:

$$T = \left( \begin{array}{rlllr} 1.54993 & -0.00000 & -9.638... ....00000 & ~~0.00000 & ~~0.00000 & 2.48762 \end{array} \right).$$

The generalized eigenvalues are:

$$\left( \begin{array}{lll} -3.68011 & + 1.08052 \times 10^{... ...- 2.26545\,i \\ -4.36974 \times 10^{-1} \end{array} \right).$$