Example 2 (from Program LA_GEES_EXAMPLE)

Matrix $A$ as in Example 1.

Function SELECT is:

 		 LOGICAL FUNCTION SELECT(X,Y) 


USE LA_PRECISION, ONLY: WP $=>$ wp 


INTRINSIC EPSILON 


REAL(WP), INTENT(IN) :: X,Y 

! 		 		 Select the real eigenvalues 

! 		 		 within the working precision 


IF (ABS(Y) $<=$ EPSILON(1.0_WP)) THEN 


SELECT = .TRUE. 


ELSE 


SELECT = .FALSE. 


END IF 


END FUNCTION SELECT

The call:
CALL LA_GEES( A, WR, WI, VS, SELECT, SDIM, INFO )

${\bf A}$, ${\bf WR}$, ${\bf WI}$, ${\bf VS}$, ${\bf SDIM}$, and ${\bf INFO}$ on exit:

$$\begin{array}{c} {\bf A} \\ \begin{array}{\vert lllll\ver... ...mes 10^{1} & \;\;\:4.45961 \\ \hline \end{array} \end{array}$$

$$\begin{array}{c} {\bf WR} \\ \begin{array}{\vert r\vert} ... ...61 \\ 3.80078 \\ -3.80078 \\ \hline \end{array} \end{array}$$

$$\begin{array}{c} {\bf VS} \\ \par\begin{array}{\vert r@{\hs... ...} & -3.02161 \times 10^{-1} \\ \hline \end{array} \end{array}$$

$${\bf SDIM} = 1, \hspace{5mm} {\bf INFO} = 0$$

The real-Schur form $T$, the matrix of Schur vectors $Z$, and the eigenvalues of matrix $A$ are:

$$T = \left( \begin{array}{rlrlr} -5.48541 & -1.53935 & -1.02... ...00000 & ~~1.00533 \times 10^{1} & 4.45961 \end{array} \right),$$

$$Z = \left( \begin{array}{@{\hspace{1mm}}r@{\hspace{1mm}}r@{... ... \times 10^{-1} & -3.02161 \times 10^{-1} \end{array} \right),$$

and

$$\left( \begin{array}{l} -5.48541 \\ -2.21691 + 8.59661i \... ... 3.80078i \\ \;\;\; 4.45961 - 3.80078i \end{array} \right).$$