test_eigen_test 28-Mar-2019 10:42:57 test_eigen_test MATLAB version 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 : 0.6 0.4 -0.4 0.4 0.4 2 : -0.4 0.9 0.1 -0.1 -0.1 3 : -0.4 -0.1 0.433333 0.566667 0.566667 4 : -0.4 -0.1 -0.566667 0.566667 -0.433333 5 : -0.4 -0.1 -0.566667 -0.433333 0.566667 The matrix Q'Q: Col: 1 2 3 4 5 Row 1 : 1 -4.21885e-17 -1.37298e-16 2.07242e-17 9.62193e-18 2 :-4.21885e-17 1 -1.95769e-16 2.15198e-16 2.05484e-16 3 :-1.37298e-16 -1.95769e-16 1 -1.08185e-16 -1.28539e-16 4 : 2.07242e-17 2.15198e-16 -1.08185e-16 1 4.20898e-16 5 : 9.62193e-18 2.05484e-16 -1.28539e-16 4.20898e-16 1 R8SYMM_GEN_TEST R8SYMM_GEN generates an arbitrary size symmetric matrix with known eigenvalues and eigenvectors. LAMBDA_MIN = -1.83804 LAMBDA_MAX = 3.64456 Lambda bins: Index Lower Limit Count Upper Limit 0 0 -1.83804 1 -1.83804 1 -1.28978 2 -1.28978 5 -0.74152 3 -0.74152 6 -0.193259 4 -0.193259 8 0.355001 5 0.355001 25 0.903262 6 0.903262 21 1.45152 7 1.45152 13 1.99978 8 1.99978 13 2.54804 9 2.54804 6 3.0963 10 3.0963 1 3.64456 11 3.64456 1 LAMBDA versus column norms of A*Q: 1: 2.679040 2.679040 2: 0.527231 0.527231 3: 0.433940 0.433940 4: 0.768876 0.768876 5: 2.212934 2.212934 6: 1.535037 1.535037 7: 2.269381 2.269381 8: 2.049543 2.049543 9: -0.666087 0.666087 10: -0.865228 0.865228 11: -1.242464 1.242464 12: 1.735809 1.735809 13: 1.039675 1.039675 14: -0.350736 0.350736 15: 1.673068 1.673068 16: 1.007775 1.007775 17: 0.724873 0.724873 18: 1.374940 1.374940 19: 3.164005 3.164005 20: 1.185600 1.185600 21: 1.297785 1.297785 22: 0.536242 0.536242 23: 3.044536 3.044536 24: 1.096577 1.096577 25: 2.398819 2.398819 26: 0.142606 0.142606 27: -0.242985 0.242985 28: 2.674516 2.674516 29: 0.932916 0.932916 30: 1.620783 1.620783 31: 0.205604 0.205604 32: 0.675837 0.675837 33: 0.476232 0.476232 34: 1.156483 1.156483 35: 0.649433 0.649433 36: 0.752243 0.752243 37: 1.131700 1.131700 38: -0.820756 0.820756 39: 1.537380 1.537380 40: 2.248567 2.248567 41: 0.293584 0.293584 42: 1.780995 1.780995 43: 0.366553 0.366553 44: 1.750902 1.750902 45: 0.610616 0.610616 46: -0.715215 0.715215 47: 0.369065 0.369065 48: 2.970035 2.970035 49: 1.280416 1.280416 50: 0.446734 0.446734 51: 0.424510 0.424510 52: -1.287907 1.287907 53: 1.385542 1.385542 54: -1.169278 1.169278 55: 0.723680 0.723680 56: 1.715245 1.715245 57: 1.039125 1.039125 58: 0.541106 0.541106 59: 0.384708 0.384708 60: 1.407113 1.407113 61: 0.671167 0.671167 62: 0.864788 0.864788 63: -1.838041 1.838041 64: 0.980327 0.980327 65: -0.710951 0.710951 66: 2.848552 2.848552 67: 2.017792 2.017792 68: -0.253012 0.253012 69: 3.644565 3.644565 70: 1.290992 1.290992 71: 2.460521 2.460521 72: 2.276552 2.276552 73: 2.054968 2.054968 74: 1.982082 1.982082 75: 1.409949 1.409949 76: 2.727823 2.727823 77: 1.361448 1.361448 78: 0.078964 0.078964 79: 1.222025 1.222025 80: 2.007899 2.007899 81: 0.878680 0.878680 82: 0.283714 0.283714 83: 1.777794 1.777794 84: -0.000438 0.000438 85: 1.282882 1.282882 86: 0.818117 0.818117 87: 2.123548 2.123548 88: 1.215752 1.215752 89: 0.682151 0.682151 90: 2.167249 2.167249 91: 0.776590 0.776590 92: 0.606361 0.606361 93: 1.734715 1.734715 94: 2.110094 2.110094 95: 1.588917 1.588917 96: 0.866045 0.866045 97: 0.254638 0.254638 98: 1.210978 1.210978 99: 0.231283 0.231283 100: 1.509619 1.509619 R8NSYMM_GEN_TEST R8NSYMM_GEN generates an arbitrary size nonsymmetric matrix with known eigenvalues and eigenvectors. LAMBDA_MIN = -1.83804 LAMBDA_MAX = 3.64456 Lambda bins: Index Lower Limit Count Upper Limit 0 0 -1.83804 1 -1.83804 1 -1.28978 2 -1.28978 5 -0.74152 3 -0.74152 6 -0.193259 4 -0.193259 8 0.355001 5 0.355001 25 0.903262 6 0.903262 21 1.45152 7 1.45152 13 1.99978 8 1.99978 13 2.54804 9 2.54804 6 3.0963 10 3.0963 1 3.64456 11 3.64456 1 LAMBDA versus column norms of A*QR: 1: 2.679040 2.679040 2: 0.527231 0.527231 3: 0.433940 0.433940 4: 0.768876 0.768876 5: 2.212934 2.212934 6: 1.535037 1.535037 7: 2.269381 2.269381 8: 2.049543 2.049543 9: -0.666087 0.666087 10: -0.865228 0.865228 11: -1.242464 1.242464 12: 1.735809 1.735809 13: 1.039675 1.039675 14: -0.350736 0.350736 15: 1.673068 1.673068 16: 1.007775 1.007775 17: 0.724873 0.724873 18: 1.374940 1.374940 19: 3.164005 3.164005 20: 1.185600 1.185600 21: 1.297785 1.297785 22: 0.536242 0.536242 23: 3.044536 3.044536 24: 1.096577 1.096577 25: 2.398819 2.398819 26: 0.142606 0.142606 27: -0.242985 0.242985 28: 2.674516 2.674516 29: 0.932916 0.932916 30: 1.620783 1.620783 31: 0.205604 0.205604 32: 0.675837 0.675837 33: 0.476232 0.476232 34: 1.156483 1.156483 35: 0.649433 0.649433 36: 0.752243 0.752243 37: 1.131700 1.131700 38: -0.820756 0.820756 39: 1.537380 1.537380 40: 2.248567 2.248567 41: 0.293584 0.293584 42: 1.780995 1.780995 43: 0.366553 0.366553 44: 1.750902 1.750902 45: 0.610616 0.610616 46: -0.715215 0.715215 47: 0.369065 0.369065 48: 2.970035 2.970035 49: 1.280416 1.280416 50: 0.446734 0.446734 51: 0.424510 0.424510 52: -1.287907 1.287907 53: 1.385542 1.385542 54: -1.169278 1.169278 55: 0.723680 0.723680 56: 1.715245 1.715245 57: 1.039125 1.039125 58: 0.541106 0.541106 59: 0.384708 0.384708 60: 1.407113 1.407113 61: 0.671167 0.671167 62: 0.864788 0.864788 63: -1.838041 1.838041 64: 0.980327 0.980327 65: -0.710951 0.710951 66: 2.848552 2.848552 67: 2.017792 2.017792 68: -0.253012 0.253012 69: 3.644565 3.644565 70: 1.290992 1.290992 71: 2.460521 2.460521 72: 2.276552 2.276552 73: 2.054968 2.054968 74: 1.982082 1.982082 75: 1.409949 1.409949 76: 2.727823 2.727823 77: 1.361448 1.361448 78: 0.078964 0.078964 79: 1.222025 1.222025 80: 2.007899 2.007899 81: 0.878680 0.878680 82: 0.283714 0.283714 83: 1.777794 1.777794 84: -0.000438 0.000438 85: 1.282882 1.282882 86: 0.818117 0.818117 87: 2.123548 2.123548 88: 1.215752 1.215752 89: 0.682151 0.682151 90: 2.167249 2.167249 91: 0.776590 0.776590 92: 0.606361 0.606361 93: 1.734715 1.734715 94: 2.110094 2.110094 95: 1.588917 1.588917 96: 0.866045 0.866045 97: 0.254638 0.254638 98: 1.210978 1.210978 99: 0.231283 0.231283 100: 1.509619 1.509619 test_eigen_test Normal end of execution. 28-Mar-2019 10:42:58 diary off