ztgsyl example program

This example solves the generalized Sylvester equations

\begin{matrix} A R - L B & = α C \\ D R - L E & = α F, \end{matrix}

where

A = (\begin{array}{r} 4.0 + 4.0 i & 1.0 + 1.0 i & 1.0 + 1.0 i & 2.0 - 1.0 i \\ 0 & 2.0 + 1.0 i & 1.0 + 1.0 i & 1.0 + 1.0 i \\ 0 & 0 & 2.0 - 1.0 i & 1.0 + 1.0 i \\ 0 & 0 & 0 & 6.0 - 2.0 i \end{array}),

B = (\begin{array}{r} 2.0 & 1.0 + 1.0 i & 1.0 + 1.0 i & 3.0 - 1.0 i \\ 0 & 1.0 & 2.0 + 1.0 i & 1.0 + 1.0 i \\ 0 & 0 & 1.0 & 1.0 + 1.0 i \\ 0 & 0 & 0 & 2.0 \end{array}),

D = (\begin{array}{r} 1.0 + 1.0 i & 1.0 - 1.0 i & 1.0 + 1.0 i & 1.0 - 1.0 i \\ 0 & 6.0 - 4.0 i & 1.0 - 1.0 i & 1.0 + 1.0 i \\ 0 & 0 & 2.0 + 4.0 i & 1.0 - 1.0 i \\ 0 & 0 & 0 & 2.0 + 3.0 i \end{array}),

E = (\begin{array}{r} 1.0 & 1.0 + 1.0 i & 1.0 - 1.0 i & 1.0 + 1.0 i \\ 0 & 2.0 & 1.0 + 1.0 i & 1.0 - 1.0 i \\ 0 & 0 & 2.0 & 1.0 + 1.0 i \\ 0 & 0 & 0 & 1.0 \end{array}),

C = (\begin{array}{r} - 13.0 + 9.0 i & 2.0 + 8.0 i & - 2.0 + 8.0 i & - 2.0 + 5.0 i \\ - 9.0 - 1.0 i & 0.0 + 5.0 i & - 7.0 - 3.0 i & - 6.0 - 0.0 i \\ - 1.0 + 1.0 i & 4.0 + 2.0 i & 4.0 - 5.0 i & 9.0 - 5.0 i \\ - 6.0 + 6.0 i & 9.0 + 1.0 i & - 2.0 + 4.0 i & 22.0 - 8.0 i \end{array})

and

F = (\begin{array}{r} - 6.0 + 5.0 i & 4.0 - 4.0 i & - 3.0 + 11.0 i & 3.0 - 7.0 i \\ - 5.0 + 11.0 i & 12.0 - 4.0 i & - 2.0 + 2.0 i & 0.0 + 14.0 i \\ - 5.0 - 1.0 i & 0.0 + 4.0 i & - 2.0 + 10.0 i & 3.0 - 1.0 i \\ - 6.0 - 2.0 i & 1.0 + 1.0 i & - 7.0 - 3.0 i & 4.0 + 7.0 i \end{array}) .

Example program for ztgsyl