Example 1 (from Program LA_HPGV_EXAMPLE)

$$A = \left( \begin{array}{lllll} 0 & \;\;\;9 -2i & \;\;\;5 ... ...\;7 +\;\:i& -4 - \;\:i & -11 & \;\;\;\;9 \end{array} \right),$$

$$B = \left( \begin{array}{lllll} \;\;\;10 & -\;1 -4i & -\;2... ...& \;\;\;\;1 & -\;1 & -\;1+\;\:i & \;\;\;11 \end{array} \right)$$

Arrays ${\bf AP}$ and ${\bf BP}$ on entry:

$$\begin{array}{cc} {\bf AP} \\ \begin{array}{\vert ccccccc... ...,0) & (3,-1) & (-9,-1) \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf AP\ continued} \\ \begin{array}{cc... ... (-4,1) & (-11,0) & (9,0) \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf BP} \\ \begin{array}{\vert ccccccc... ...10,0) & (-6,4) & (0,1) \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf BP\ continued} \\ \begin{array}{cc... ...-1,0) & (-1,-1) & (11,0) \\ \hline \end{array} \end{array}$$

The call:
CALL LA_HPGV( AP, BP, W )

BP and W on exit:

$$\begin{array}{cc} {\bf BP} \\ \begin{array}{\vert ccc} \h... ...26491) & (3.04959,0.00000) \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf BP\ continued} \\ \begin{array}{c@{\... ...^{-1}) & (2.90532,0.00000) \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf BP\ continued} \\ \begin{array}{ccc}... ...675,-1.36939 \times 10^{-1}) \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf BP\ continued} \\ \begin{array}{ccc}... ...{-1},1.63957 \times 10^{-1}) \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf BP\ continued} \\ \begin{array}{ccc\... ...^{-1}) & (2.80072,0.00000) \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf W} \\ \begin{array}{\vert l\vert} ... ...\; 1.56312 \\ \;\;\; 16.6680 \\ \hline \end{array} \end{array}$$

The eigenvalues of the problem $A\, z=\lambda \, B\, z$ are:

$$\left( \begin{array}{l} -1.02534 \\ -4.96729 \times 10^{-1} ... ...{-1} \\ \;\;\; 1.56312 \\ \;\;\; 16.6680 \end{array} \right).$$

The triangular factor $U$ of the Cholesky factorization of $B$ is:

$$U = \left( \begin{array}{lll} 3.16228 & -3.16228 \times 10^{... ...0.00000 & \;\;\: 0.00000 & \;\;\: 0.00000 \end{array} \right.$$

$$\left. \begin{array}{ll} -1.89737 \hspace{1.17 cm} + 1.26491... ...{-1}i \\ \;\;\: 0.00000 & \;\;\: 2.80072 \end{array} \right).$$