ztgsen example program

This example reorders the generalized Schur factors

S

and

T

and update the matrices

Q

and

Z

given by

S = (\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}),

T = (\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}),

Q = (\begin{array}{r} 1.0 & 0 & 0 & 0 \\ 0 & 1.0 & 0 & 0 \\ 0 & 0 & 1.0 & 0 \\ 0 & 0 & 0 & 1.0 \end{array}) and Z = (\begin{array}{r} 1.0 & 0 & 0 & 0 \\ 0 & 1.0 & 0 & 0 \\ 0 & 0 & 1.0 & 0 \\ 0 & 0 & 0 & 1.0 \end{array}),

selecting the second and third generalized eigenvalues to be moved to the leading positions. Bases for the left and right deflating subspaces, and estimates of the condition numbers for the eigenvalues and Frobenius norm based bounds on the condition numbers for the deflating subspaces are also output.

Example program for ztgsen