Example 2 (from Program LA_GGES_EXAMPLE)

Matrices $A$ and $B$ as in Example 1.

Function SELECT is:

 		 LOGICAL FUNCTION SELECT( ALPHAR, ALPHAI, BETA ) 


USE LA_PRECISION, ONLY: WP $=>$ wp 


REAL(WP), INTENT(IN) :: ALPHAR, ALPHAI, BETA 


INTRINSIC EPSILON, ABS 


IF ( ABS(BETA) $>$ EPSILON(1.0_WP) ) THEN 


IF ( ABS(ALPHAI/BETA) $<$ 3.0_WP) THEN 


SELECT = .TRUE. 


ELSE 


SELECT = .FALSE. 


END IF 


ELSE 


SELECT = .FALSE. 


END IF 


END FUNCTION SELECT

The call:

   CALL LA_GGES( A, B, ALPHAR, ALPHAI, BETA, VSL, VSR, & 


SELECT, SDIM, INFO )

A, B, ALPHAR, ALPHAI, BETA, VSL, VSR, SDIM and INFO on exit:

$$\begin{array}{cc} {\bf A} \\ \begin{array}{\vert lllll\ve... ...\;\;\:8.68772 \times 10^{-1} \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf B} \\ \begin{array}{\vert lllll\ve... ...00 & -4.05673 \times 10^{-1} \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf ALPHAR} \\ \begin{array}{\vert rrr... ...{-1} -5.08116 \times 10^{-1} \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf ALPHAI} \\ \begin{array}{\vert rrr... ...0.00000 & 1.49188 & -1.49188 \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf BETA} \\ \begin{array}{\vert rrrrr... ...-1} & 1.38071 \times 10^{-1} \\ \hline \end{array} \end{array}$$

$$\begin{array}{c} {\bf VSL} \\ \begin{array}{\vert rrrrr\ver... ...\;\:3.48258 \times 10^{-1} \\ \hline \end{array} \end{array}$$

$$\begin{array}{c} {\bf VSR} \\ \begin{array}{\vert rrrrr\ver... ...\;\:6.20156 \times 10^{-1} \\ \hline \end{array} \end{array}$$

$$\begin{array}{cc} {\bf SDIM} = 3 & {\bf INFO} = 0 \end{array}$$

The block upper triangular matrix $S$ is:

$$S = \left( \begin{array}{lllll} 2.17189 & 6.00538 & \;\;\:... ...13023 & \;\;\:8.68772 \times 10^{-1} \\ \end{array} \right) .$$

The upper triangular matrix $T$ is:

$$T = \left( \begin{array}{lllll} 3.57463 & \;\;\:0.00000 & ... ...\;\:0.00000 & -4.05673 \times 10^{-1} \\ \end{array} \right).$$

The left Schur vectors are:

$$\left( \begin{array}{rrrrr} \;\;\:2.18104 \times 10^{-1} & ... ... 10^{-1} & \;\;\:3.48258 \times 10^{-1} \end{array} \right).$$

The right Schur vectors are:

$$\left( \begin{array}{rrrrr} \;\;\:1.64796 \times 10^{-1} &... ... 10^{-2} & \;\;\:6.20156 \times 10^{-1} \end{array} \right).$$

The selected eigenvalues are:

$$\left( \begin{array}{l} -5.65687 \times 10^{-1} + 2.26545\... ... - 2.26545\,i \\ -4.36974 \times 10^{-1} \end{array} \right)$$