Home License -- for personal use only. Not for government, academic, research, commercial, or other organizational use. 13-May-2025 18:36:34 test_eigen_test(): MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7 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 : 0.173535 0.169849 0.552588 0.262576 0.752819 2 : -0.591897 -0.180784 -0.521973 0.41417 0.415911 3 : 0.729056 0.18068 -0.612415 0.165045 0.18314 4 : -0.278272 0.744716 -0.189081 -0.532476 0.220637 5 : 0.102883 -0.592639 -0.106711 -0.669885 0.421972 The matrix Q'Q (should be identity): Col: 1 2 3 4 5 Row 1 : 1 1.249e-16 5.20417e-18 -8.32667e-17 6.93889e-17 2 : 1.249e-16 1 6.93889e-17 2.22045e-16 -1.11022e-16 3 : 5.20417e-18 6.93889e-17 1 -4.16334e-17 1.66533e-16 4 :-8.32667e-17 2.22045e-16 -4.16334e-17 1 -5.55112e-17 5 : 6.93889e-17 -1.11022e-16 1.66533e-16 -5.55112e-17 1 r8symm_gen_test(): r8symm_gen() generates an arbitrary size symmetric matrix with known eigenvalues and eigenvectors. LAMBDA_MIN = 3.96257 LAMBDA_MAX = 18.1512 Lambda bins: Index Lower Limit Count Upper Limit 0 0 3.96257 1 3.96257 1 5.38143 2 5.38143 1 6.80029 3 6.80029 0 8.21915 4 8.21915 1 9.63801 5 9.63801 0 11.0569 6 11.0569 2 12.4757 7 12.4757 3 13.8946 8 13.8946 1 15.3135 9 15.3135 0 16.7323 10 16.7323 0 18.1512 11 18.1512 1 LAMBDA versus column norms of A*Q: 1: 13.357486 13.357486 2: 3.962565 3.962565 3: 13.586193 13.586193 4: 18.151176 18.151176 5: 12.444469 12.444469 6: 15.173465 15.173465 7: 13.634426 13.634426 8: 8.482795 8.482795 9: 11.469357 11.469357 10: 6.063586 6.063586 r8nsymm_gen_test(): r8nsymm_gen() generates an arbitrary size nonsymmetric matrix with known eigenvalues and eigenvectors. LAMBDA_MIN = 0.334885 LAMBDA_MAX = 12.4498 Lambda bins: Index Lower Limit Count Upper Limit 0 0 0.334885 1 0.334885 1 1.54638 2 1.54638 0 2.75787 3 2.75787 0 3.96937 4 3.96937 0 5.18086 5 5.18086 1 6.39236 6 6.39236 0 7.60385 7 7.60385 0 8.81534 8 8.81534 1 10.0268 9 10.0268 1 11.2383 10 11.2383 0 12.4498 11 12.4498 1 The matrix A: 6.7496 5.3761 -3.3051 -1.9837 7.8743 5.6624 3.4662 -3.9870 -3.5376 -2.2272 3.0110 -0.6422 3.5038 -2.6945 2.4791 -10.2390 16.3823 2.6372 8.2498 11.8214 -10.0507 11.5698 1.9191 9.5430 16.1472 The matrix Q: 0.5536 0.0749 0.2826 0.7555 -0.1932 0.4382 -0.0395 0.2500 -0.1959 0.8400 -0.3927 -0.3893 -0.3946 0.5867 0.4408 -0.0507 0.8893 -0.3748 0.1438 0.2133 -0.5871 0.2247 0.7493 0.1613 0.1315 The matrix T: 0.3349 7.8052 1.0266 14.2019 5.5598 0 10.5005 7.2774 11.5176 6.9984 0 0 12.4498 13.6968 18.5594 0 0 0 9.0294 -0.6918 0 0 0 0 5.8021 The eigenvalues LAMBDA (sorted): 0.3349 5.8021 9.0294 10.5005 12.4498 Q' * T * Q should equal A 6.7496 5.3761 -3.3051 -1.9837 7.8743 5.6624 3.4662 -3.9870 -3.5376 -2.2272 3.0110 -0.6422 3.5038 -2.6945 2.4791 -10.2390 16.3823 2.6372 8.2498 11.8214 -10.0507 11.5698 1.9191 9.5430 16.1472 test_eigen_test(): Normal end of execution. 13-May-2025 18:36:34