Example program for ztgevc

This example computes the α and β arguments, which defines the generalized eigenvalues and the corresponding left and right eigenvectors, of the matrix pair A,B given by
A = 1.0+3.0i 1.0+4.0i 1.0+5.0i 1.0+6.0i 2.0+2.0i 4.0+3.0i 8.0+4.0i 16.0+5.0i 3.0+1.0i 9.0+2.0i 27.0+3.0i 81.0+4.0i 4.0+0.0i 16.0+1.0i 64.0+2.0i 256.0+3.0i  
and
B = 1.0+0.0i 2.0+1.0i 3.0+2.0i 4.0+3.0i 1.0+1.0i 4.0+2.0i 9.0+3.0i 16.0+4.0i 1.0+2.0i 8.0+3.0i 27.0+4.0i 64.0+5.0i 1.0+3.0i 16.0+4.0i 81.0+5.0i 256.0+6.0i .  
To compute generalized eigenvalues, it is required to call five routines: zggbal to balance the matrix, zgeqrf to perform the QR factorization of B, zunmqr to apply Q to A, zgghrd to reduce the matrix pair to the generalized Hessenberg form and zhgeqz to compute the eigenvalues via the QZ algorithm.
The computation of generalized eigenvectors is done by calling ztgevc to compute the eigenvectors of the balanced matrix pair. The routine zggbak is called to backward transform the eigenvectors to the user-supplied matrix pair. If both left and right eigenvectors are required then zggbak must be called twice.