F08VQF Example Program Results
Number of infinite generalized singular values (K)
2
Number of finite generalized singular values (L)
2
Numerical rank of (A**T B**T)**T (K+L)
4
Finite generalized singular values
2.0720E+00 1.1058E+00
Unitary matrix U
1 2
1 ( -1.3038E-02, -3.2595E-01) ( -1.4039E-01, -2.6167E-01)
2 ( 4.2764E-01, -6.2582E-01) ( 8.6298E-02, -3.8174E-02)
3 ( -3.2595E-01, 1.6428E-01) ( 3.8163E-01, -1.8219E-01)
4 ( 1.5906E-01, -5.2151E-03) ( -2.8207E-01, 1.9732E-01)
5 ( -1.7210E-01, -1.3038E-02) ( -5.0942E-01, -5.0319E-01)
6 ( -2.6336E-01, -2.4772E-01) ( -1.0861E-01, 2.8474E-01)
3 4
1 ( 2.5177E-01, -7.9789E-01) ( -5.0956E-02, -2.1750E-01)
2 ( -3.2188E-01, 1.6112E-01) ( 1.1979E-01, 1.6319E-01)
3 ( 1.3231E-01, -1.4565E-02) ( -5.0671E-01, 1.8615E-01)
4 ( 2.1598E-01, 1.8813E-01) ( -4.0163E-01, 2.6787E-01)
5 ( 3.6488E-02, 2.0316E-01) ( 1.9271E-01, 1.5574E-01)
6 ( 1.0906E-01, -1.2712E-01) ( -8.8159E-02, 5.6169E-01)
5 6
1 ( -4.5947E-02, 1.4052E-04) ( -5.2773E-02, -2.2492E-01)
2 ( -8.0311E-02, -4.3605E-01) ( -3.8117E-02, -2.1907E-01)
3 ( 5.9714E-02, -5.8974E-01) ( -1.3850E-01, -9.0941E-02)
4 ( -4.6443E-02, 3.0864E-01) ( -3.7354E-01, -5.5148E-01)
5 ( 5.7843E-01, -1.2439E-01) ( -1.8815E-02, -5.5686E-02)
6 ( 1.5763E-02, 4.7130E-02) ( 6.5007E-01, 4.9173E-03)
Unitary matrix V
1 2
1 ( 9.8930E-01, 1.0471E-19) ( -1.1461E-01, 9.0250E-02)
2 ( -1.1461E-01, -9.0250E-02) ( -9.8930E-01, 1.0471E-19)
Unitary matrix Q
1 2
1 ( 7.0711E-01, 0.0000E+00) ( 0.0000E+00, 0.0000E+00)
2 ( 0.0000E+00, 0.0000E+00) ( 7.0711E-01, 0.0000E+00)
3 ( 7.0711E-01, 0.0000E+00) ( 0.0000E+00, 0.0000E+00)
4 ( 0.0000E+00, 0.0000E+00) ( 7.0711E-01, 0.0000E+00)
3 4
1 ( 6.9954E-01, -1.1784E-18) ( 8.1044E-02, -6.3817E-02)
2 ( -8.1044E-02, -6.3817E-02) ( 6.9954E-01, 1.1784E-18)
3 ( -6.9954E-01, 1.1784E-18) ( -8.1044E-02, 6.3817E-02)
4 ( 8.1044E-02, 6.3817E-02) ( -6.9954E-01, -1.1784E-18)
Nonsingular upper triangular matrix R
1 2
1 ( -2.7118E+00, 0.0000E+00) ( -1.4390E+00, -1.0315E+00)
2 ( -1.8583E+00, 0.0000E+00)
3
4
3 4
1 ( -7.6930E-02, 1.3613E+00) ( -2.8137E-01, -3.2425E-02)
2 ( -1.0760E+00, 3.1016E-02) ( 1.3292E+00, 3.6772E-01)
3 ( 3.2537E+00, 0.0000E+00) ( -6.3858E-17, 3.4216E-33)
4 ( -2.1084E+00, 0.0000E+00)
Estimate of reciprocal condition number for R
1.3E-01
Error estimate for the generalized singular values
8.3E-16