06-Jun-2023 10:22:32 test_eigen_test(): MATLAB/Octave version 5.2.0 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 : -0.819757 -0.0846323 -0.042627 0.555377 -0.102834 2 : 0.36642 -0.62768 -0.16856 0.324619 -0.581346 3 : -0.282234 -0.0058135 -0.769228 -0.520845 -0.239414 4 : -0.335011 -0.388725 0.59013 -0.559328 -0.27488 5 : 0.0429653 0.669114 0.172642 0.0452945 -0.720128 The matrix Q'Q: Col: 1 2 3 4 5 Row 1 : 1 6.93889e-18 -1.12757e-17 5.09575e-17 4.51028e-17 2 : 6.93889e-18 1 -8.32667e-17 6.245e-17 0 3 :-1.12757e-17 -8.32667e-17 1 2.35922e-16 5.55112e-17 4 : 5.09575e-17 6.245e-17 2.35922e-16 1 1.249e-16 5 : 4.51028e-17 0 5.55112e-17 1.249e-16 1 r8symm_gen_test(): r8symm_gen() generates an arbitrary size symmetric matrix with known eigenvalues and eigenvectors. LAMBDA_MIN = -1.78982 LAMBDA_MAX = 3.93395 Lambda bins: Index Lower Limit Count Upper Limit 0 0 -1.78982 1 -1.78982 1 -1.21744 2 -1.21744 5 -0.645065 3 -0.645065 7 -0.0726882 4 -0.0726882 19 0.499689 5 0.499689 16 1.07207 6 1.07207 25 1.64444 7 1.64444 13 2.21682 8 2.21682 8 2.7892 9 2.7892 5 3.36157 10 3.36157 0 3.93395 11 3.93395 1 LAMBDA versus column norms of A*Q: 1: 3.933952 3.933952 2: -0.879178 0.879178 3: 1.006590 1.006590 4: 2.607169 2.607169 5: 1.344848 1.344848 6: -0.975994 0.975994 7: 1.549045 1.549045 8: -0.516687 0.516687 9: 0.290596 0.290596 10: 1.754474 1.754474 11: 1.455144 1.455144 12: 2.158178 2.158178 13: 2.933734 2.933734 14: 0.415024 0.415024 15: 0.301533 0.301533 16: 1.507141 1.507141 17: 1.574215 1.574215 18: 1.738495 1.738495 19: 2.049092 2.049092 20: -0.153298 0.153298 21: 1.192910 1.192910 22: 3.025662 3.025662 23: 0.054211 0.054211 24: 0.203638 0.203638 25: 1.516874 1.516874 26: 1.282492 1.282492 27: 0.702523 0.702523 28: 0.907866 0.907866 29: -0.131894 0.131894 30: 2.099290 2.099290 31: 0.309665 0.309665 32: 0.838654 0.838654 33: 2.302499 2.302499 34: 1.585357 1.585357 35: 0.426870 0.426870 36: 0.236675 0.236675 37: -0.364095 0.364095 38: 0.489015 0.489015 39: -0.370312 0.370312 40: -0.997915 0.997915 41: 1.763000 1.763000 42: 1.983477 1.983477 43: 0.685010 0.685010 44: 0.916523 0.916523 45: 1.722269 1.722269 46: 1.813236 1.813236 47: 1.480374 1.480374 48: 0.260000 0.260000 49: 0.242112 0.242112 50: 0.005324 0.005324 51: -0.755128 0.755128 52: 1.182766 1.182766 53: 1.381304 1.381304 54: 1.571049 1.571049 55: 0.275745 0.275745 56: -0.730861 0.730861 57: 1.632358 1.632358 58: 1.735930 1.735930 59: 2.485403 2.485403 60: 1.180763 1.180763 61: 1.226330 1.226330 62: 3.002766 3.002766 63: -0.062383 0.062383 64: 2.613456 2.613456 65: 2.645225 2.645225 66: 0.689597 0.689597 67: 3.304055 3.304055 68: 1.234908 1.234908 69: 1.196320 1.196320 70: 0.236511 0.236511 71: 0.868289 0.868289 72: 2.292266 2.292266 73: 1.372707 1.372707 74: 1.127320 1.127320 75: 1.591933 1.591933 76: 0.785624 0.785624 77: 0.919586 0.919586 78: 3.245660 3.245660 79: -0.331487 0.331487 80: 0.970262 0.970262 81: 0.802315 0.802315 82: -1.789820 1.789820 83: 0.921903 0.921903 84: 0.849608 0.849608 85: 0.734432 0.734432 86: 0.262991 0.262991 87: 1.589485 1.589485 88: 0.977929 0.977929 89: 0.118917 0.118917 90: -0.072991 0.072991 91: 1.141418 1.141418 92: 1.462992 1.462992 93: 1.863180 1.863180 94: 1.195984 1.195984 95: 0.161940 0.161940 96: 1.872280 1.872280 97: 2.242249 2.242249 98: 2.316621 2.316621 99: 0.115298 0.115298 100: 2.055065 2.055065 r8nsymm_gen_test(): r8nsymm_gen() generates an arbitrary size nonsymmetric matrix with known eigenvalues and eigenvectors. LAMBDA_MIN = -0.882073 LAMBDA_MAX = 3.01687 Lambda bins: Index Lower Limit Count Upper Limit 0 0 -0.882073 1 -0.882073 4 -0.492179 2 -0.492179 9 -0.102285 3 -0.102285 6 0.28761 4 0.28761 14 0.677504 5 0.677504 17 1.0674 6 1.0674 11 1.45729 7 1.45729 21 1.84719 8 1.84719 5 2.23708 9 2.23708 9 2.62698 10 2.62698 3 3.01687 11 3.01687 1 LAMBDA versus column norms of A*QR: 1: 1.413845 1.413845 2: 0.509275 0.509275 3: 2.490589 2.490589 4: -0.305337 0.305337 5: 0.687125 0.687125 6: 1.840118 1.840118 7: 0.733922 0.733922 8: -0.245768 0.245768 9: 1.240881 1.240881 10: 0.273674 0.273674 11: 1.498039 1.498039 12: 0.419744 0.419744 13: 1.505870 1.505870 14: 0.695253 0.695253 15: 1.562405 1.562405 16: 0.001934 0.001934 17: 0.416781 0.416781 18: 1.884645 1.884645 19: 1.286301 1.286301 20: 1.848643 1.848643 21: 0.378245 0.378245 22: 1.202651 1.202651 23: 1.702840 1.702840 24: 0.446164 0.446164 25: -0.268968 0.268968 26: 1.475137 1.475137 27: 1.316060 1.316060 28: 0.641920 0.641920 29: 1.635543 1.635543 30: 2.396717 2.396717 31: 1.030022 1.030022 32: -0.750943 0.750943 33: -0.552739 0.552739 34: 0.889073 0.889073 35: 1.437859 1.437859 36: 2.290887 2.290887 37: 0.378368 0.378368 38: 2.431256 2.431256 39: 1.492456 1.492456 40: 0.723198 0.723198 41: 1.499414 1.499414 42: 1.592362 1.592362 43: 1.279354 1.279354 44: 1.880284 1.880284 45: 0.057947 0.057947 46: 1.268201 1.268201 47: 1.514685 1.514685 48: 2.153947 2.153947 49: 1.524066 1.524066 50: 2.728025 2.728025 51: 1.022489 1.022489 52: 1.496329 1.496329 53: 0.331299 0.331299 54: 0.425915 0.425915 55: 0.835288 0.835288 56: 0.303286 0.303286 57: 1.022877 1.022877 58: 2.852510 2.852510 59: 0.963648 0.963648 60: 1.201331 1.201331 61: 0.932539 0.932539 62: -0.882073 0.882073 63: 1.254756 1.254756 64: -0.141926 0.141926 65: 1.517717 1.517717 66: 0.266652 0.266652 67: 2.546812 2.546812 68: 0.570930 0.570930 69: -0.229412 0.229412 70: 1.187522 1.187522 71: -0.129206 0.129206 72: 0.781130 0.781130 73: 2.591836 2.591836 74: 1.793262 1.793262 75: 3.010691 3.010691 76: 0.846701 0.846701 77: 3.016870 3.016870 78: 1.496429 1.496429 79: 1.539814 1.539814 80: 1.683783 1.683783 81: 2.532355 2.532355 82: -0.335179 0.335179 83: 0.821596 0.821596 84: 0.571336 0.571336 85: 0.286172 0.286172 86: -0.735730 0.735730 87: -0.237571 0.237571 88: 2.465307 2.465307 89: 1.766763 1.766763 90: 1.589092 1.589092 91: 0.153840 0.153840 92: 1.544436 1.544436 93: 0.892613 0.892613 94: 0.814467 0.814467 95: 1.032720 1.032720 96: 2.447016 2.447016 97: -0.151514 0.151514 98: 2.032687 2.032687 99: 0.575258 0.575258 100: 0.567667 0.567667 test_eigen_test(): Normal end of execution. 06-Jun-2023 10:22:32