F08YXF Example Program Results
Matrix A after balancing
1 2 3 4
1 ( 1.0000, 3.0000) ( 1.0000, 4.0000) ( 0.1000, 0.5000) ( 0.1000, 0.6000)
2 ( 2.0000, 2.0000) ( 4.0000, 3.0000) ( 0.8000, 0.4000) ( 1.6000, 0.5000)
3 ( 0.3000, 0.1000) ( 0.9000, 0.2000) ( 0.2700, 0.0300) ( 0.8100, 0.0400)
4 ( 0.4000, 0.0000) ( 1.6000, 0.1000) ( 0.6400, 0.0200) ( 2.5600, 0.0300)
Matrix B after balancing
1 2 3 4
1 ( 1.0000, 0.0000) ( 2.0000, 1.0000) ( 0.3000, 0.2000) ( 0.4000, 0.3000)
2 ( 1.0000, 1.0000) ( 4.0000, 2.0000) ( 0.9000, 0.3000) ( 1.6000, 0.4000)
3 ( 0.1000, 0.2000) ( 0.8000, 0.3000) ( 0.2700, 0.0400) ( 0.6400, 0.0500)
4 ( 0.1000, 0.3000) ( 1.6000, 0.4000) ( 0.8100, 0.0500) ( 2.5600, 0.0600)
Matrix A in Hessenberg form
1 2 3 4
1 ( -2.868, -1.595) ( -0.809, -0.328) ( -4.900, -0.987) ( -0.048, 1.163)
2 ( -2.672, 0.595) ( -0.790, 0.049) ( -4.955, -0.163) ( -0.439, -0.574)
3 ( 0.000, 0.000) ( -0.098, -0.011) ( -1.168, -0.137) ( -1.756, -0.205)
4 ( 0.000, 0.000) ( 0.000, 0.000) ( 0.087, 0.004) ( 0.032, 0.001)
Matrix B in Hessenberg form
1 2 3 4
1 ( -1.775, 0.000) ( -0.721, 0.043) ( -5.021, 1.190) ( -0.145, 0.726)
2 ( 0.000, 0.000) ( -0.218, 0.035) ( -2.541, -0.146) ( -0.823, -0.418)
3 ( 0.000, 0.000) ( 0.000, 0.000) ( -1.396, -0.163) ( -1.747, -0.204)
4 ( 0.000, 0.000) ( 0.000, 0.000) ( 0.000, 0.000) ( -0.100, -0.004)
Minimal required LWORK = 4
Actual value of LWORK = 24
Generalized eigenvalues
1 ( -0.635, 1.653)
2 ( 0.458, -0.843)
3 ( 0.674, -0.050)
4 ( 0.493, 0.910)
Right eigenvectors
1 2 3 4
1 ( 1.0000,-0.0000) ( 1.0000, 0.0000) ( 1.0000,-0.0000) ( 1.0000, 0.0000)
2 (-0.8639,-0.2796) (-1.6440,-0.0550) (-1.0246, 0.1861) (-1.9996,-0.1245)
3 ( 0.3132, 0.1060) ( 0.9119, 0.2267) ( 0.1281,-0.0133) ( 1.1549,-0.0127)
4 (-0.0518,-0.0122) (-0.1487,-0.1000) ( 0.0067,-0.0022) (-0.2130, 0.0682)
Left eigenvectors
1 2 3 4
1 ( 1.0000, 0.0000) ( 1.0000,-0.0000) ( 1.0000,-0.0000) ( 1.0000,-0.0000)
2 (-0.7857, 0.3499) (-2.1501, 0.0091) (-1.6147, 0.8923) (-2.0208, 0.9724)
3 ( 0.2535,-0.1483) ( 1.2377, 0.0697) ( 0.2769,-0.1860) ( 1.0247,-0.7718)
4 (-0.0297, 0.0264) (-0.2257,-0.0827) (-0.0344, 0.0282) (-0.1346, 0.2047)