DGGESX 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}
3.9 & 12.5 & -34.5 & -0.5 ...
...
4.3 & 21.5 & -43.5 & 3.5 \\
4.4 & 26.0 & -46.0 & 6.0
\end{array} }\right.$$\displaystyle \begin{array}{rrrr}
3.9 & 12.5 & -34.5 & -0.5 \\
4.3 & 21.5 &...
... 7.5 \\
4.3 & 21.5 & -43.5 & 3.5 \\
4.4 & 26.0 & -46.0 & 6.0
\end{array}$$\displaystyle \left.\vphantom{
\begin{array}{rrrr}
3.9 & 12.5 & -34.5 & -0.5 ...
...
4.3 & 21.5 & -43.5 & 3.5 \\
4.4 & 26.0 & -46.0 & 6.0
\end{array} }\right)$   and  B = $\displaystyle \left(\vphantom{
\begin{array}{rrrr}
1.0 & 2.0 & -3.0 & 1.0 \\ ...
...\\
1.0 & 3.0 & -4.0 & 3.0 \\
1.0 & 3.0 & -4.0 & 4.0
\end{array} }\right.$$\displaystyle \begin{array}{rrrr}
1.0 & 2.0 & -3.0 & 1.0 \\
1.0 & 3.0 & -5.0 & 4.0 \\
1.0 & 3.0 & -4.0 & 3.0 \\
1.0 & 3.0 & -4.0 & 4.0
\end{array}$$\displaystyle \left.\vphantom{
\begin{array}{rrrr}
1.0 & 2.0 & -3.0 & 1.0 \\ ...
...\\
1.0 & 3.0 & -4.0 & 3.0 \\
1.0 & 3.0 & -4.0 & 4.0
\end{array} }\right)$,

such that the real eigenvalues of $ \left(\vphantom{A, B}\right.$A, B$ \left.\vphantom{A, B}\right)$ 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