Example 2 (from Program LA_HPGV_EXAMPLE)

Matrices $A$ and $B$ as in Example 1.
Arrays ${\bf AP}$ and ${\bf BP}$ on entry:

$$\begin{array}{cc} {\bf AP} \\ \begin{array}{\vert ccccccc... ...) & (2,-3) & (-9,1) \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf AP\ continued} \\ \begin{array}{cc... ...7, 0) & (-11, 0) & (9, 0) \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf BP} \\ \begin{array}{\vert ccccccc... ...1,-1) & (11,0) & (1,2) \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf BP\ continued} \\ \begin{array}{cc... ...(12,0) & (-1,1) & (11,0) \\ \hline \end{array} \end{array}$$

The call:
CALL LA_HPGV( AP, BP, W, 3, 'L', Z, INFO )

${\bf BP}$, ${\bf W}$, ${\bf Z}$, and ${\bf INFO}$ on exit:

$$\begin{array}{cc} {\bf BP} \\ \begin{array}{\vert ccc} \h... ...}, 9.48683 \times 10^{-1}) \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf BP\ continued} \\ \begin{array}{ccc... ...-1}) & (3.04959, 0.00000) \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf BP\ continued} \\ \begin{array}{c@{... ..., -1.63956 \times 10^{-1}) \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf BP\ continued} \\ \begin{array}{ccc... ..., -1.07330 \times 10^{-1}) \\ \hline \end{array} \end{array}$$

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

$$\begin{array}{c} {\bf W} \\ \begin{array}{\vert r\vert} \... ...80 \\ 111.573 \\ 391.493 \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf Z} \\ \begin{array}{\vert ll} \hli... ...s 10^{-1}, \;\;\; 1.63311) \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf Z} \\ \begin{array}{ll} \hline (\;... ...\; 6.16168 \times 10^{-1}) \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf Z\ continued} \\ \begin{array}{l\v... ...457) \\ (-1.68730, -1.47214)\\ \hline \end{array} \end{array}$$

$${\bf INFO} = 0$$

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

$$\left( \begin{array}{r} -203.206 \\ -35.5916 \\ 1.73180 \\ 111.573 \\ 391.493 \end{array} \right).$$

The eigenvectors are:

$$\left( \begin{array}{ll} \;\;\; 2.42010 & -1.00862 \times ... ...\; 3.00437 \times 10^{-1} + 1.63311i \\ \end{array} \right.$$

$$\left. \begin{array}{ll} \;\;\; 2.60276 \times 10^{-1} & -... ...\times 10^{-2} + 6.16168 \times 10^{-1}i \end{array} \right.$$

$$\left. \begin{array}{l} -1.34162 \\ -1.11936 - 1.08115i ... ...26824 + 1.97457i \\ -1.68730 - 1.47214i \end{array} \right) .$$

The triangular factor $L$ from the Cholesky factorization of $B$ is:

$$L= \left( \begin{array}{ll} \;\;\: 3.16228 \\ -3.16228 \tim... ...7 \times 10^{-1} - 1.63956 \times 10^{-1}i \end{array} \right.$$

$$\left. \begin{array}{lll} \\ \\ \;\;\; 2.90532 \\ \;\;... ...57555 + 4.29493 \times 10^{-1}i & 2.80072 \end{array} \right).$$