04-Jun-2024 15:56:37 test_eigen_test(): MATLAB/Octave version 6.4.0 Test test_eigen(). r8mat_orth_uniform_test(): r8symm_orth_uniform() generates a random orthogopnal matrix. The matrix Q: Col: 1 2 3 4 5 Row 1 : -0.766228 0.157799 -0.277686 -0.536732 0.15101 2 : -0.143115 -0.679037 -0.630949 0.343893 0.0454665 3 : -0.0566975 0.530457 -0.450085 0.284904 -0.657004 4 : -0.120072 -0.482264 0.30908 -0.337687 -0.737185 5 : -0.612194 0.00669894 0.476116 0.631232 0.00579999 The matrix Q'Q (should be identity): Col: 1 2 3 4 5 Row 1 : 1 -4.66368e-17 -9.66878e-17 -1.35987e-16 -1.31833e-16 2 :-4.66368e-17 1 -2.98802e-16 2.09424e-16 -1.91814e-17 3 :-9.66878e-17 -2.98802e-16 1 9.97227e-17 9.55462e-17 4 :-1.35987e-16 2.09424e-16 9.97227e-17 1 5.83369e-17 5 :-1.31833e-16 -1.91814e-17 9.55462e-17 5.83369e-17 1 r8symm_gen_test(): r8symm_gen() generates an arbitrary size symmetric matrix with known eigenvalues and eigenvectors. LAMBDA_MIN = 2.52818 LAMBDA_MAX = 23.7799 Lambda bins: Index Lower Limit Count Upper Limit 0 0 2.52818 1 2.52818 1 4.65335 2 4.65335 1 6.77853 3 6.77853 1 8.9037 4 8.9037 4 11.0289 5 11.0289 0 13.1541 6 13.1541 0 15.2792 7 15.2792 1 17.4044 8 17.4044 1 19.5296 9 19.5296 0 21.6548 10 21.6548 0 23.7799 11 23.7799 1 LAMBDA versus column norms of A*Q: 1: 7.710713 7.710713 2: 10.552144 10.552144 3: 4.876003 4.876003 4: 18.595285 18.595285 5: 9.952591 9.952591 6: 23.779926 23.779926 7: 10.256885 10.256885 8: 10.586150 10.586150 9: 2.528176 2.528176 10: 17.249330 17.249330 r8nsymm_gen_test(): r8nsymm_gen() generates an arbitrary size nonsymmetric matrix with known eigenvalues and eigenvectors. LAMBDA_MIN = 7.2431 LAMBDA_MAX = 16.6386 Lambda bins: Index Lower Limit Count Upper Limit 0 0 7.2431 1 7.2431 1 8.18264 2 8.18264 1 9.12219 3 9.12219 1 10.0617 4 10.0617 0 11.0013 5 11.0013 0 11.9408 6 11.9408 0 12.8804 7 12.8804 0 13.8199 8 13.8199 0 14.7595 9 14.7595 0 15.699 10 15.699 1 16.6386 11 16.6386 1 The matrix A: 3.8752 -2.7049 3.9888 -0.7843 9.5311 10.1530 7.6279 9.0620 3.4852 14.5532 2.3077 -2.4978 6.7236 -4.2452 -7.1877 0.4524 4.2943 -2.7911 11.7977 -2.1403 2.0571 -2.0393 14.7282 9.3124 28.1504 The matrix Q: -1.9225e-02 -2.7729e-01 6.6722e-01 -5.4365e-01 -4.2662e-01 2.9819e-02 -9.2429e-01 -2.6039e-01 2.4819e-01 -1.2410e-01 -5.7818e-01 1.8766e-01 6.9523e-03 4.4779e-01 -6.5568e-01 5.9244e-01 1.7746e-01 -4.5692e-01 -1.9424e-01 -6.0912e-01 -5.5988e-01 -4.5724e-02 -5.2744e-01 -6.3608e-01 4.0619e-02 The matrix T: 15.7500 4.4221 7.1122 13.7736 11.3427 0 9.5448 14.6143 8.2795 12.0609 0 0 16.6386 18.9786 5.5170 0 0 0 8.9984 6.4812 0 0 0 0 7.2431 The eigenvalues LAMBDA (sorted): 7.2431 8.9984 9.5448 15.7500 16.6386 Q' * T * Q should equal A 3.8752 -2.7049 3.9888 -0.7843 9.5311 10.1530 7.6279 9.0620 3.4852 14.5532 2.3077 -2.4978 6.7236 -4.2452 -7.1877 0.4524 4.2943 -2.7911 11.7977 -2.1403 2.0571 -2.0393 14.7282 9.3124 28.1504 test_eigen_test(): Normal end of execution. 04-Jun-2024 15:56:37