F08YKF Example Program Results
Matrix A after balancing
1 2 3 4 5
1 1.0000 1.0000 0.1000 0.1000 0.1000
2 2.0000 4.0000 0.8000 1.6000 3.2000
3 0.3000 0.9000 0.2700 0.8100 2.4300
4 0.4000 1.6000 0.6400 2.5600 10.2400
5 0.5000 2.5000 1.2500 6.2500 31.2500
Matrix B after balancing
1 2 3 4 5
1 1.0000 2.0000 0.3000 0.4000 0.5000
2 1.0000 4.0000 0.9000 1.6000 2.5000
3 0.1000 0.8000 0.2700 0.6400 1.2500
4 0.1000 1.6000 0.8100 2.5600 6.2500
5 0.1000 3.2000 2.4300 10.2400 31.2500
Matrix A in Hessenberg form
1 2 3 4 5
1 -2.1898 -0.3181 2.0547 4.7371 -4.6249
2 -0.8395 -0.0426 1.7132 7.5194 -17.1850
3 0.0000 -0.2846 -1.0101 -7.5927 26.4499
4 0.0000 0.0000 0.0376 1.4070 -3.3643
5 0.0000 0.0000 0.0000 0.3813 -0.9937
Matrix B in Hessenberg form
1 2 3 4 5
1 -1.4248 -0.3476 2.1175 5.5813 -3.9269
2 0.0000 -0.0782 0.1189 8.0940 -15.2928
3 0.0000 0.0000 1.0021 -10.9356 26.5971
4 0.0000 0.0000 0.0000 0.5820 -0.0730
5 0.0000 0.0000 0.0000 0.0000 0.5321
Minimal required LWORK = 5
Actual value of LWORK = 30
Generalized eigenvalues
1 ( -2.437, 0.000)
2 ( 0.607, 0.795)
3 ( 0.607, -0.795)
4 ( 1.000, 0.000)
5 ( -0.410, 0.000)
Right eigenvectors
1 2 3 4 5
1 1.0000 1.0000 1.0000 1.0000 1.0000
2 -2.1481 -0.8592 3.4364 -1.8286 -1.9586
3 2.0253 0.2587 -1.7998 1.3500 1.4395
4 -0.8863 -0.0386 0.5356 -0.3571 -0.4589
5 0.1422 0.0027 -0.0810 0.0500 0.0512
Left eigenvectors
1 2 3 4 5
1 1.0000 1.0000 1.0000 1.0000 1.0000
2 -1.9586 -0.7813 -21.5866 -1.8286 -2.1481
3 1.4395 0.2214 10.1913 1.3500 2.0253
4 -0.4589 -0.0282 -2.8094 -0.3571 -0.8863
5 0.0512 0.0012 0.4063 0.0500 0.1422