ZGGESX Example

To find the generalized Schur factorization of the matrix pair $ \left(\vphantom{A, B}\right.$A, B$ \left.\vphantom{A, B}\right)$, where

A = $\displaystyle \left(\vphantom{
\begin{array}{rrrr}
-21.10 - 22.50i & 53.50 - ...
....40i & 14.40 + 43.30i & -32.50 - 46.00i & -19.00 - 32.50i
\end{array} }\right.$$\displaystyle \begin{array}{rrrr}
-21.10 - 22.50i & 53.50 - 50.50i & -34.50 + ...
... 5.50 + 4.40i & 14.40 + 43.30i & -32.50 - 46.00i & -19.00 - 32.50i
\end{array}$$\displaystyle \left.\vphantom{
\begin{array}{rrrr}
-21.10 - 22.50i & 53.50 - ...
....40i & 14.40 + 43.30i & -32.50 - 46.00i & -19.00 - 32.50i
\end{array} }\right)$

and

B = $\displaystyle \left(\vphantom{
\begin{array}{rrrr}
1.00 - 5.00i & 1.60 + 1.20...
....00 + 1.00i & -1.80 + 2.40i & 0.00 - 4.00i & 4.00 - 5.00i
\end{array} }\right.$$\displaystyle \begin{array}{rrrr}
1.00 - 5.00i & 1.60 + 1.20i & -3.00 + 0.00i ...
...i \\
0.00 + 1.00i & -1.80 + 2.40i & 0.00 - 4.00i & 4.00 - 5.00i
\end{array}$$\displaystyle \left.\vphantom{
\begin{array}{rrrr}
1.00 - 5.00i & 1.60 + 1.20...
....00 + 1.00i & -1.80 + 2.40i & 0.00 - 4.00i & 4.00 - 5.00i
\end{array} }\right)$,

such that the eigenvalues of $ \left(\vphantom{A, B}\right.$A, B$ \left.\vphantom{A, B}\right)$ for which $ \left\vert\vphantom{\lambda}\right.$$ \lambda$$ \left.\vphantom{\lambda}\right\vert$ < 6 correspond to the top left diagonal elements of the generalized Schur form, $ \left(\vphantom{S, T}\right.$S, T$ \left.\vphantom{S, T}\right)$. Estimates of the condition numbers for the selected eigenvalue cluster and corresponding deflating subspaces are also returned.

Example program
Example data
Example results