03-Feb-2021 09:15:56 test_eigen_test MATLAB/Octave version 9.9.0.1467703 (R2020b) 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: Col: 1 2 3 4 5 Row 1 : 1 1.50312e-16 3.27644e-17 -8.15839e-17 5.64495e-17 2 : 1.50312e-16 1 7.71234e-17 2.13185e-16 -9.11076e-17 3 : 3.27644e-17 7.71234e-17 1 -9.29948e-18 1.74183e-16 4 :-8.15839e-17 2.13185e-16 -9.29948e-18 1 -8.37644e-17 5 : 5.64495e-17 -9.11076e-17 1.74183e-16 -8.37644e-17 1 R8SYMM_GEN_TEST R8SYMM_GEN generates an arbitrary size symmetric matrix with known eigenvalues and eigenvectors. LAMBDA_MIN = -1.11292 LAMBDA_MAX = 3.54193 Lambda bins: Index Lower Limit Count Upper Limit 0 0 -1.11292 1 -1.11292 6 -0.64744 2 -0.64744 7 -0.181955 3 -0.181955 15 0.283531 4 0.283531 8 0.749016 5 0.749016 25 1.2145 6 1.2145 16 1.67999 7 1.67999 17 2.14547 8 2.14547 2 2.61096 9 2.61096 2 3.07644 10 3.07644 1 3.54193 11 3.54193 1 LAMBDA versus column norms of A*Q: 1: 1.895654 1.895654 2: 1.204412 1.204412 3: 1.523431 1.523431 4: 0.769549 0.769549 5: 1.042798 1.042798 6: 0.120672 0.120672 7: 0.399459 0.399459 8: 1.482817 1.482817 9: 1.436772 1.436772 10: 1.808710 1.808710 11: 1.817722 1.817722 12: 1.165770 1.165770 13: 2.535546 2.535546 14: 1.458399 1.458399 15: 1.961696 1.961696 16: -0.933524 0.933524 17: 0.650799 0.650799 18: 1.778613 1.778613 19: 1.312106 1.312106 20: 1.068624 1.068624 21: 0.055723 0.055723 22: 1.869493 1.869493 23: 1.204833 1.204833 24: 0.298251 0.298251 25: -0.827786 0.827786 26: 1.117711 1.117711 27: 0.229000 0.229000 28: -0.011082 0.011082 29: 1.024400 1.024400 30: 0.171643 0.171643 31: 0.314112 0.314112 32: -0.450546 0.450546 33: 1.480018 1.480018 34: 1.784553 1.784553 35: -1.063214 1.063214 36: 1.021208 1.021208 37: 0.845810 0.845810 38: 1.241667 1.241667 39: 1.169548 1.169548 40: 2.021090 2.021090 41: 0.975792 0.975792 42: 1.755911 1.755911 43: 0.632848 0.632848 44: -0.108064 0.108064 45: 1.465027 1.465027 46: 0.878392 0.878392 47: 1.707242 1.707242 48: 1.840020 1.840020 49: 0.908027 0.908027 50: 2.948132 2.948132 51: 0.984153 0.984153 52: 1.588854 1.588854 53: 1.026071 1.026071 54: 1.640477 1.640477 55: 0.774882 0.774882 56: 1.309915 1.309915 57: 0.987717 0.987717 58: 2.803626 2.803626 59: 0.029517 0.029517 60: 1.164424 1.164424 61: 1.703080 1.703080 62: -0.263274 0.263274 63: 0.015029 0.015029 64: 0.681854 0.681854 65: 0.907163 0.907163 66: 1.405283 1.405283 67: 1.017474 1.017474 68: 0.254380 0.254380 69: -0.265929 0.265929 70: 0.425329 0.425329 71: 3.141860 3.141860 72: 1.755194 1.755194 73: 1.205110 1.205110 74: -0.106652 0.106652 75: 1.253103 1.253103 76: 1.269209 1.269209 77: -0.042662 0.042662 78: 1.203039 1.203039 79: -0.549417 0.549417 80: 3.541927 3.541927 81: 1.523901 1.523901 82: -0.834011 0.834011 83: -0.503432 0.503432 84: 0.727541 0.727541 85: -0.520102 0.520102 86: -0.133606 0.133606 87: 0.073497 0.073497 88: -0.346482 0.346482 89: 0.989980 0.989980 90: 0.137269 0.137269 91: 2.091657 2.091657 92: 1.634740 1.634740 93: 2.468727 2.468727 94: 0.110558 0.110558 95: 1.889506 1.889506 96: -0.723821 0.723821 97: 2.112560 2.112560 98: 0.972975 0.972975 99: -1.112925 1.112925 100: 1.795704 1.795704 R8NSYMM_GEN_TEST R8NSYMM_GEN generates an arbitrary size nonsymmetric matrix with known eigenvalues and eigenvectors. LAMBDA_MIN = -1.01561 LAMBDA_MAX = 3.92989 Lambda bins: Index Lower Limit Count Upper Limit 0 0 -1.01561 1 -1.01561 9 -0.521059 2 -0.521059 11 -0.0265093 3 -0.0265093 10 0.46804 4 0.46804 13 0.962589 5 0.962589 20 1.45714 6 1.45714 17 1.95169 7 1.95169 10 2.44624 8 2.44624 8 2.94079 9 2.94079 1 3.43534 10 3.43534 0 3.92989 11 3.92989 1 LAMBDA versus column norms of A*QR: 1: 1.934809 1.934809 2: 2.736909 2.736909 3: 1.951545 1.951545 4: 1.178515 1.178515 5: 0.467686 0.467686 6: -0.103080 0.103080 7: 1.181960 1.181960 8: 3.072730 3.072730 9: 1.734965 1.734965 10: 2.393530 2.393530 11: 1.474078 1.474078 12: -0.425162 0.425162 13: 1.248898 1.248898 14: -0.532462 0.532462 15: -0.025203 0.025203 16: 0.633146 0.633146 17: 1.117168 1.117168 18: 0.216469 0.216469 19: 1.295332 1.295332 20: 1.348739 1.348739 21: 1.252312 1.252312 22: 1.630467 1.630467 23: 2.853409 2.853409 24: 2.909859 2.909859 25: 2.388599 2.388599 26: 2.447610 2.447610 27: 0.946787 0.946787 28: 1.361981 1.361981 29: 0.777922 0.777922 30: 0.737818 0.737818 31: 0.649576 0.649576 32: 1.387192 1.387192 33: 1.651919 1.651919 34: 2.568802 2.568802 35: 0.964621 0.964621 36: 2.100139 2.100139 37: 2.531976 2.531976 38: 1.150144 1.150144 39: 2.002996 2.002996 40: 0.759590 0.759590 41: 1.569725 1.569725 42: 1.028447 1.028447 43: 0.394774 0.394774 44: 1.738264 1.738264 45: -1.015608 1.015608 46: 0.471424 0.471424 47: -0.316043 0.316043 48: 0.858067 0.858067 49: 1.290540 1.290540 50: 1.396719 1.396719 51: 2.203054 2.203054 52: 1.467938 1.467938 53: 0.760041 0.760041 54: -0.368274 0.368274 55: -0.078392 0.078392 56: -0.882105 0.882105 57: -0.269900 0.269900 58: 0.094771 0.094771 59: -0.788491 0.788491 60: 1.755644 1.755644 61: 1.388419 1.388419 62: 3.929885 3.929885 63: -0.628625 0.628625 64: 0.883296 0.883296 65: 0.004511 0.004511 66: 2.443069 2.443069 67: 0.347195 0.347195 68: 1.393750 1.393750 69: -0.851695 0.851695 70: 2.531304 2.531304 71: 1.556554 1.556554 72: -0.086878 0.086878 73: 1.673056 1.673056 74: -0.389531 0.389531 75: 2.005743 2.005743 76: 1.357682 1.357682 77: -0.390772 0.390772 78: 0.128339 0.128339 79: 1.384302 1.384302 80: 2.149505 2.149505 81: 1.319048 1.319048 82: -0.661531 0.661531 83: 1.606253 1.606253 84: 1.772804 1.772804 85: 0.334372 0.334372 86: 1.474047 1.474047 87: 0.670613 0.670613 88: -0.197588 0.197588 89: 2.345978 2.345978 90: 1.121990 1.121990 91: -0.915303 0.915303 92: -0.233597 0.233597 93: 2.138083 2.138083 94: 0.434640 0.434640 95: -0.538634 0.538634 96: 2.530558 2.530558 97: 1.840219 1.840219 98: 1.710146 1.710146 99: 0.700020 0.700020 100: 0.667075 0.667075 test_eigen_test Normal end of execution. 03-Feb-2021 09:15:56