08-Jan-2022 10:26:47 test_eigen_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 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 = -1.94428 LAMBDA_MAX = 3.58549 Lambda bins: Index Lower Limit Count Upper Limit 0 0 -1.94428 1 -1.94428 1 -1.39131 2 -1.39131 3 -0.838329 3 -0.838329 5 -0.285352 4 -0.285352 22 0.267626 5 0.267626 13 0.820604 6 0.820604 22 1.37358 7 1.37358 16 1.92656 8 1.92656 11 2.47954 9 2.47954 5 3.03251 10 3.03251 1 3.58549 11 3.58549 1 LAMBDA versus column norms of A*Q: 1: 1.671497 1.671497 2: -0.207487 0.207487 3: 1.717239 1.717239 4: 2.630235 2.630235 5: 1.488894 1.488894 6: 2.034693 2.034693 7: 1.726885 1.726885 8: 0.696559 0.696559 9: 1.293871 1.293871 10: 0.212717 0.212717 11: 1.888396 1.888396 12: -0.147070 0.147070 13: -0.068870 0.068870 14: 0.190501 0.190501 15: -1.944284 1.944284 16: 2.438380 2.438380 17: 1.325191 1.325191 18: 0.245072 0.245072 19: 2.370299 2.370299 20: -0.711516 0.711516 21: 0.897758 0.897758 22: 0.758553 0.758553 23: 1.319207 1.319207 24: 1.312859 1.312859 25: 0.135120 0.135120 26: 0.969949 0.969949 27: 0.835121 0.835121 28: 1.627707 1.627707 29: 2.093266 2.093266 30: 2.109273 2.109273 31: 0.136347 0.136347 32: 1.077359 1.077359 33: -0.214117 0.214117 34: -0.113501 0.113501 35: 0.993151 0.993151 36: 2.532630 2.532630 37: 0.230334 0.230334 38: 1.371379 1.371379 39: 0.774416 0.774416 40: 2.117356 2.117356 41: -0.089064 0.089064 42: 1.032557 1.032557 43: 1.552527 1.552527 44: 2.100610 2.100610 45: 2.544212 2.544212 46: 1.085931 1.085931 47: -0.491590 0.491590 48: 0.257698 0.257698 49: -0.061582 0.061582 50: 3.350457 3.350457 51: 0.384398 0.384398 52: 1.748077 1.748077 53: 0.807581 0.807581 54: 1.888610 1.888610 55: 0.235151 0.235151 56: -0.402269 0.402269 57: -0.422376 0.422376 58: 1.488194 1.488194 59: 0.822625 0.822625 60: 0.803947 0.803947 61: 2.419310 2.419310 62: 1.291584 1.291584 63: 1.197811 1.197811 64: 2.587699 2.587699 65: 0.195534 0.195534 66: 1.696624 1.696624 67: 1.835088 1.835088 68: 0.756285 0.756285 69: 1.215670 1.215670 70: -0.165844 0.165844 71: -0.147953 0.147953 72: 1.104875 1.104875 73: 1.722254 1.722254 74: 3.585491 3.585491 75: 0.333109 0.333109 76: 1.187331 1.187331 77: 0.917506 0.917506 78: -0.933023 0.933023 79: 0.561034 0.561034 80: -0.794679 0.794679 81: 1.840376 1.840376 82: 0.111968 0.111968 83: 1.100093 1.100093 84: 0.455471 0.455471 85: 1.303521 1.303521 86: 0.399673 0.399673 87: 1.489965 1.489965 88: 1.739363 1.739363 89: 2.711888 2.711888 90: 0.805876 0.805876 91: -1.138355 1.138355 92: 0.160411 0.160411 93: 2.354594 2.354594 94: -0.072155 0.072155 95: 1.960954 1.960954 96: 1.124050 1.124050 97: 2.436697 2.436697 98: -0.960900 0.960900 99: 0.802302 0.802302 100: -0.207845 0.207845 r8nsymm_gen_test(): r8nsymm_gen() generates an arbitrary size nonsymmetric matrix with known eigenvalues and eigenvectors. LAMBDA_MIN = -1.18191 LAMBDA_MAX = 3.75134 Lambda bins: Index Lower Limit Count Upper Limit 0 0 -1.18191 1 -1.18191 6 -0.688587 2 -0.688587 11 -0.195262 3 -0.195262 17 0.298064 4 0.298064 17 0.791389 5 0.791389 19 1.28471 6 1.28471 13 1.77804 7 1.77804 9 2.27136 8 2.27136 4 2.76469 9 2.76469 2 3.25802 10 3.25802 1 3.75134 11 3.75134 1 LAMBDA versus column norms of A*QR: 1: -0.622579 0.622579 2: -0.000072 0.000072 3: 1.447118 1.447118 4: 0.224159 0.224159 5: 0.914666 0.914666 6: 1.369391 1.369391 7: -0.386211 0.386211 8: 0.149750 0.149750 9: 0.250618 0.250618 10: 0.198211 0.198211 11: 0.560751 0.560751 12: 1.787179 1.787179 13: 0.492529 0.492529 14: 1.694311 1.694311 15: 1.340327 1.340327 16: 1.191856 1.191856 17: 1.975032 1.975032 18: 3.140161 3.140161 19: 2.467333 2.467333 20: -0.584034 0.584034 21: 1.529912 1.529912 22: -0.246844 0.246844 23: -1.010796 1.010796 24: -0.210709 0.210709 25: -1.181912 1.181912 26: -0.131275 0.131275 27: 2.354297 2.354297 28: 0.523513 0.523513 29: 3.680722 3.680722 30: 1.390817 1.390817 31: 2.003997 2.003997 32: 0.854006 0.854006 33: 0.720422 0.720422 34: 0.216632 0.216632 35: 1.160817 1.160817 36: -0.482935 0.482935 37: 0.149934 0.149934 38: -0.069225 0.069225 39: 1.168338 1.168338 40: 2.515902 2.515902 41: 3.157529 3.157529 42: -0.755702 0.755702 43: 1.346747 1.346747 44: 0.345899 0.345899 45: -0.081478 0.081478 46: 1.103380 1.103380 47: 0.528136 0.528136 48: 1.051119 1.051119 49: 1.768506 1.768506 50: 0.064519 0.064519 51: 0.847289 0.847289 52: -0.700357 0.700357 53: 0.616747 0.616747 54: 1.988852 1.988852 55: -0.745698 0.745698 56: 1.390851 1.390851 57: -0.352000 0.352000 58: 1.218994 1.218994 59: 0.549708 0.549708 60: 0.721471 0.721471 61: -0.603889 0.603889 62: 0.088931 0.088931 63: 0.806979 0.806979 64: 1.071679 1.071679 65: 0.808687 0.808687 66: 0.358770 0.358770 67: 2.328555 2.328555 68: 0.805537 0.805537 69: 0.224103 0.224103 70: 0.241353 0.241353 71: 0.924401 0.924401 72: 1.929004 1.929004 73: 0.575432 0.575432 74: 1.871566 1.871566 75: 1.226524 1.226524 76: 0.436674 0.436674 77: 0.182778 0.182778 78: 1.177344 1.177344 79: 0.896673 0.896673 80: 0.095009 0.095009 81: 0.205657 0.205657 82: 1.539128 1.539128 83: 1.521664 1.521664 84: 0.688600 0.688600 85: 1.826128 1.826128 86: 0.650059 0.650059 87: 0.884497 0.884497 88: 2.234822 2.234822 89: 0.460079 0.460079 90: -1.042955 1.042955 91: -0.288880 0.288880 92: 1.290849 1.290849 93: 0.784208 0.784208 94: 3.751340 3.751340 95: -0.415077 0.415077 96: 0.756131 0.756131 97: 1.040251 1.040251 98: -0.373829 0.373829 99: 2.079187 2.079187 100: 1.743931 1.743931 test_eigen_test(): Normal end of execution. 08-Jan-2022 10:26:48