Tue Oct 19 17:23:23 2021 test_eigen_test(): Python version: 3.6.9 Test test_eigen(). r8vec_house_column_test Python version: 3.6.9 r8vec_house_column returns the compact form of a Householder matrix that "packs" a column of a matrix. Matrix A: Col: 0 1 2 3 Row 0 : 4.33856 1.20535 1.8877 1.32896 1 : 2.69631 4.75622 4.38123 4.53689 2 : 0.17385 0.136787 1.30788 0.0314573 3 : 1.55001 4.40085 2.27952 1.20969 Working on column K = 0 Householder matrix H: Col: 0 1 2 3 Row 0 : -0.812317 -0.504836 -0.0325502 -0.290212 1 : -0.504836 0.859374 -0.00906713 -0.0808408 2 : -0.0325502 -0.00906713 0.999415 -0.00521236 3 : -0.290212 -0.0808408 -0.00521236 0.953528 Product H*A: Col: 0 1 2 3 Row 0 : -5.34097 -4.66186 -4.44933 -3.72201 1 : -3.08578e-16 3.12186 2.616 3.1299 2 : -5.56332e-17 0.0314089 1.19406 -0.0592608 3 : -4.97907e-16 3.46131 1.26475 0.400867 Working on column K = 1 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 -0.669741 -0.00673823 -0.742564 2 : 0 -0.00673823 0.999973 -0.00299661 3 : 0 -0.742564 -0.00299661 0.669768 Product H*A: Col: 0 1 2 3 Row 0 : -5.34097 -4.66186 -4.44933 -3.72201 1 : 5.7677e-16 -4.6613 -2.69925 -2.39349 2 : -5.20604e-17 -4.03433e-18 1.17261 -0.0815505 3 : -1.04176e-16 1.60373e-16 -1.09903 -2.05549 Working on column K = 2 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 -0.729629 0.683843 3 : 0 0 0.683843 0.729629 Product H*A: Col: 0 1 2 3 Row 0 : -5.34097 -4.66186 -4.44933 -3.72201 1 : 5.7677e-16 -4.6613 -2.69925 -2.39349 2 : -3.32556e-17 1.12614e-16 -1.60714 -1.34613 3 : -1.11611e-16 1.14254e-16 -1.47233e-17 -1.55551 r8vec_house_column_test Normal end of execution. r8mat_house_axh_test Python version: 3.6.9 r8mat_house_axh multiplies a matrix A times a compact Householder matrix. Matrix A: Col: 0 1 2 3 4 Row 0 : -2.23627 2.2334 3.56582 3.60012 -3.15125 1 : 3.04599 -1.78553 -4.43695 -2.25083 3.06558 2 : -0.166366 -0.576084 -1.96073 -4.53082 -1.24725 3 : 2.39166 2.91615 1.76121 4.30676 1.91514 4 : 3.76479 -1.16177 4.15486 -2.62225 -3.17509 Compact vector V so column 3 of H*A is packed: 0: 0 1: 0 2: -0.836212 3: 0.21403 4: 0.504917 Householder matrix H: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : 0 1 0 0 0 2 : 0 0 -0.3985 0.357949 0.844435 3 : 0 0 0.357949 0.908382 -0.216135 4 : 0 0 0.844435 -0.216135 0.490118 Indirect product A*H: Col: 0 1 2 3 4 Row 0 : -2.23627 2.2334 -2.79335 5.22776 0.688509 1 : 3.04599 -1.78553 3.55112 -4.2954 -1.75774 2 : -0.166366 -0.576084 -1.89367 -4.54798 -1.28774 3 : 2.39166 2.91615 2.45697 4.12868 1.49503 4 : 3.76479 -1.16177 -5.2755 -0.208533 2.5191 Direct product A*H: Col: 0 1 2 3 4 Row 0 : -2.23627 2.2334 -2.79335 5.22776 0.688509 1 : 3.04599 -1.78553 3.55112 -4.2954 -1.75774 2 : -0.166366 -0.576084 -1.89367 -4.54798 -1.28774 3 : 2.39166 2.91615 2.45697 4.12868 1.49503 4 : 3.76479 -1.16177 -5.2755 -0.208533 2.5191 H*A should pack column 3: Col: 0 1 2 3 4 Row 0 : -2.23627 2.2334 3.56582 3.60012 -3.15125 1 : 3.04599 -1.78553 -4.43695 -2.25083 3.06558 2 : 4.10151 0.292361 4.92028 1.13281 -1.4986 3 : 1.29929 2.69387 9.08327e-17 2.85714 1.97948 4 : 1.18778 -1.68615 -4.63692e-16 -6.04203 -3.02332 r8mat_house_axh_test Normal end of execution. r8mat_orth_uniform_test R8SYMM_orth_uniform generates a random orthogopnal matrix. The matrix Q: Col: 0 1 2 3 4 Row 0 : -0.454893 -0.642263 0.539463 0.0965502 -0.283245 1 : -0.280861 -0.425647 -0.666938 0.452717 0.300305 2 : -0.763409 0.411871 -0.269744 -0.274633 -0.315252 3 : -0.342085 0.119054 0.332543 -0.176069 0.852771 4 : -0.119895 0.471711 0.284299 0.824198 -0.0546445 The matrix Q'Q: Col: 0 1 2 3 4 Row 0 : 1 3.08759e-17 -1.74229e-16 4.15515e-17 8.37075e-17 1 : 3.08759e-17 1 -1.24905e-16 -6.50549e-18 -6.33896e-17 2 : -1.74229e-16 -1.24905e-16 1 8.05462e-17 3.29765e-17 3 : 4.15515e-17 -6.50549e-18 8.05462e-17 1 1.06411e-17 4 : 8.37075e-17 -6.33896e-17 3.29765e-17 1.06411e-17 1 r8nsymm_gen_test r8nsymm_gen makes an arbitrary size nonsymmetric matrix with known eigenvalues and eigenvectors. LAMBDA_MIN = -0.848402 LAMBDA_MAX = 3.06963 Lambda bins: Index Lower Limit Count Upper Limit 0 0 -0.848402 1 -0.848402 2 -0.456599 2 -0.456599 4 -0.0647959 3 -0.0647959 9 0.327007 4 0.327007 6 0.71881 5 0.71881 8 1.11061 6 1.11061 7 1.50242 7 1.50242 5 1.89422 8 1.89422 4 2.28602 9 2.28602 4 2.67782 10 2.67782 0 3.06963 11 3.06963 1 LAMBDA versus column norms of A*QR: 0: 0.177928 0.177928 1: -0.0439728 0.0439728 2: 1.78289 1.78289 3: 0.0686414 0.0686414 4: 0.280524 0.280524 5: 1.26889 1.26889 6: 2.01353 2.01353 7: 2.16281 2.16281 8: 0.348516 0.348516 9: 2.60694 2.60694 10: 0.880664 0.880664 11: -0.157923 0.157923 12: 1.70875 1.70875 13: 1.34212 1.34212 14: 0.417336 0.417336 15: 0.815997 0.815997 16: 0.198404 0.198404 17: 0.263284 0.263284 18: 3.06963 3.06963 19: 2.58291 2.58291 20: 1.33977 1.33977 21: 1.83775 1.83775 22: 1.56114 1.56114 23: -0.487204 0.487204 24: 2.55784 2.55784 25: 2.4928 2.4928 26: 2.13144 2.13144 27: 1.17993 1.17993 28: -0.270688 0.270688 29: 0.556319 0.556319 30: 1.91277 1.91277 31: -0.27228 0.27228 32: 0.683738 0.683738 33: -0.37517 0.37517 34: 0.938042 0.938042 35: -0.848402 0.848402 36: 0.572027 0.572027 37: 0.204155 0.204155 38: 1.22144 1.22144 39: 0.755068 0.755068 40: 0.0722288 0.0722288 41: 0.785426 0.785426 42: 1.14169 1.14169 43: 1.75406 1.75406 44: 0.0418194 0.0418194 45: 1.30734 1.30734 46: 0.752872 0.752872 47: 1.00555 1.00555 48: 1.01711 1.01711 49: 0.393513 0.393513 r8symm_gen_test r8symm_gen makes an arbitrary size symmetric matrix with known eigenvalues and eigenvectors. LAMBDA_MIN = -1.42187 LAMBDA_MAX = 2.93512 Lambda bins: Index Lower Limit Count Upper Limit 0 0 -1.42187 1 -1.42187 4 -0.98617 2 -0.98617 10 -0.55047 3 -0.55047 8 -0.114771 4 -0.114771 14 0.320928 5 0.320928 14 0.756627 6 0.756627 19 1.19233 7 1.19233 14 1.62803 8 1.62803 7 2.06373 9 2.06373 5 2.49942 10 2.49942 4 2.93512 11 2.93512 1 LAMBDA versus column norms of A*Q: 0: 0.867262 0.867262 1: 2.54762 2.54762 2: 2.36121 2.36121 3: -0.671757 0.671757 4: 0.503377 0.503377 5: 0.0486749 0.0486749 6: 0.637477 0.637477 7: 0.699188 0.699188 8: 0.790888 0.790888 9: -1.14409 1.14409 10: 1.47819 1.47819 11: 1.03799 1.03799 12: 0.162271 0.162271 13: -0.848617 0.848617 14: 0.365323 0.365323 15: -0.683712 0.683712 16: 1.3856 1.3856 17: 2.46415 2.46415 18: 1.8231 1.8231 19: 1.67695 1.67695 20: 1.0004 1.0004 21: 2.37078 2.37078 22: -1.31089 1.31089 23: 1.14362 1.14362 24: 0.160519 0.160519 25: 1.73332 1.73332 26: -0.977069 0.977069 27: -0.377962 0.377962 28: -0.889413 0.889413 29: 1.1663 1.1663 30: 1.93827 1.93827 31: 0.717485 0.717485 32: -1.42187 1.42187 33: 0.776851 0.776851 34: 0.668733 0.668733 35: 2.23539 2.23539 36: 1.24611 1.24611 37: 1.54335 1.54335 38: 2.81311 2.81311 39: -0.110891 0.110891 40: 1.31648 1.31648 41: 2.48001 2.48001 42: 0.97592 0.97592 43: 1.26189 1.26189 44: 0.0228965 0.0228965 45: -0.0963232 0.0963232 46: 0.033005 0.033005 47: 1.38846 1.38846 48: 0.980767 0.980767 49: 0.80125 0.80125 50: 2.93512 2.93512 51: -0.0425581 0.0425581 52: 1.27957 1.27957 53: 0.861079 0.861079 54: 0.72522 0.72522 55: -0.158005 0.158005 56: -0.234549 0.234549 57: -0.9457 0.9457 58: -0.136454 0.136454 59: -0.807813 0.807813 60: -0.529822 0.529822 61: 1.72206 1.72206 62: 0.674644 0.674644 63: 0.488001 0.488001 64: 1.72197 1.72197 65: 0.876411 0.876411 66: 1.31967 1.31967 67: 1.17808 1.17808 68: 1.62797 1.62797 69: 0.241092 0.241092 70: 1.98698 1.98698 71: 0.781058 0.781058 72: -0.416198 0.416198 73: 1.09037 1.09037 74: -0.557887 0.557887 75: 1.38237 1.38237 76: 0.228687 0.228687 77: 0.459454 0.459454 78: 0.00686125 0.00686125 79: 0.0857799 0.0857799 80: 0.340645 0.340645 81: 1.13766 1.13766 82: 2.6391 2.6391 83: -0.155555 0.155555 84: 2.52379 2.52379 85: -0.90331 0.90331 86: 0.643454 0.643454 87: -0.238504 0.238504 88: 0.317428 0.317428 89: 0.770662 0.770662 90: -1.00712 1.00712 91: -0.773101 0.773101 92: 0.916898 0.916898 93: 1.62458 1.62458 94: 1.09295 1.09295 95: 0.450808 0.450808 96: 1.60897 1.60897 97: 0.144896 0.144896 98: 1.25987 1.25987 99: 0.385138 0.385138 test_eigen_test(): Normal end of execution. Tue Oct 19 17:24:59 2021