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

and

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

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