Thu Sep 13 18:48:40 2018 TEST_EIGEN_TEST Python version: 3.6.5 Test the TEST_EIGEN library. R8VEC_HOUSE_COLUMN_TEST Python version: 3.6.5 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 : 1.09209 2.07654 0.219145 2.00653 1 : 4.78159 0.330594 3.16983 3.77337 2 : 4.14755 1.28789 0.308636 3.98643 3 : 2.80848 0.549784 2.24769 0.00919186 Working on column K = 0 Householder matrix H: Col: 0 1 2 3 Row 0 : -0.155781 -0.682069 -0.591626 -0.400615 1 : -0.682069 0.597486 -0.34914 -0.236418 2 : -0.591626 -0.34914 0.697156 -0.205068 3 : -0.400615 -0.236418 -0.205068 0.86114 Product H*A: Col: 0 1 2 3 Row 0 : -7.01042 -1.53117 -3.27924 -5.24844 1 : -8.88178e-16 -1.79845 1.1053 -0.508058 2 : -1.33227e-15 -0.558841 -1.48213 0.272729 3 : -8.88178e-16 -0.700714 1.03509 -2.50551 Working on column K = 1 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 -0.895014 -0.278112 -0.348717 2 : 0 -0.278112 0.959184 -0.0511776 3 : 0 -0.348717 -0.0511776 0.93583 Product H*A: Col: 0 1 2 3 Row 0 : -7.01042 -1.53117 -3.27924 -5.24844 1 : 1.47517e-15 2.00941 -0.938018 1.25258 2 : -9.85422e-16 0 -1.78201 0.531121 3 : -4.53279e-16 -5.55112e-17 0.659083 -2.18152 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 -0.937906 0.346889 3 : 0 0 0.346889 0.937906 Product H*A: Col: 0 1 2 3 Row 0 : -7.01042 -1.53117 -3.27924 -5.24844 1 : 1.47517e-15 2.00941 -0.938018 1.25258 2 : 7.66996e-16 -1.92562e-17 1.89999 -1.25489 3 : -7.66965e-16 -5.20643e-17 1.11022e-16 -1.86183 R8VEC_HOUSE_COLUMN_TEST Normal end of execution. R8MAT_HOUSE_AXH_TEST Python version: 3.6.5 R8MAT_HOUSE_AXH multiplies a matrix A times a compact Householder matrix. Matrix A: Col: 0 1 2 3 4 Row 0 : -2.81582 -4.33881 -4.38273 -4.98162 3.59097 1 : 4.56318 -2.42422 -0.50461 3.97504 3.40847 2 : 3.29509 -3.90043 -0.986937 -1.49248 -3.76896 3 : 0.616954 -4.56171 2.54673 -4.05455 -4.92488 4 : -0.846929 1.33966 2.97287 -4.86383 -2.39697 Compact vector V so column 3 of H*A is packed: 0: 0 1: 0 2: -0.788819 3: 0.399863 4: 0.466771 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 -0.244469 0.630839 0.736395 3 : 0 0 0.630839 0.680219 -0.373289 4 : 0 0 0.736395 -0.373289 0.56425 Indirect product A*H: Col: 0 1 2 3 4 Row 0 : -2.81582 -4.33881 0.573215 -7.49385 0.65837 1 : 4.56318 -2.42422 5.14095 1.11322 0.0678026 2 : 3.29509 -3.90043 -3.47568 -0.230898 -2.29629 3 : 0.616954 -4.56171 -6.80702 0.686997 0.610057 4 : -0.846929 1.33966 -5.56019 -0.538306 2.65233 Direct product A*H: Col: 0 1 2 3 4 Row 0 : -2.81582 -4.33881 0.573215 -7.49385 0.65837 1 : 4.56318 -2.42422 5.14095 1.11322 0.0678026 2 : 3.29509 -3.90043 -3.47568 -0.230898 -2.29629 3 : 0.616954 -4.56171 -6.80702 0.686997 0.610057 4 : -0.846929 1.33966 -5.56019 -0.538306 2.65233 H*A should pack column 3: Col: 0 1 2 3 4 Row 0 : -2.81582 -4.33881 -4.38273 -4.98162 3.59097 1 : 4.56318 -2.42422 -0.50461 3.97504 3.40847 2 : -1.04002 -0.937652 4.03706 -5.7746 -3.95052 3 : 2.81449 -6.06358 -4.77072e-16 -1.88388 -4.83284 4 : 1.71831 -0.41352 -6.18983e-16 -2.32995 -2.28953 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 : -0.559743 -0.371903 -0.0337166 0.68224 0.285986 1 : 0.188708 -0.906112 0.0432361 -0.368531 0.0752686 2 : -0.404357 -0.0795868 -0.732356 -0.200174 -0.503733 3 : -0.423174 0.184571 -0.114406 -0.542494 0.692437 4 : 0.555425 0.0157436 -0.668999 0.253702 0.423476 The matrix Q'Q: Col: 0 1 2 3 4 Row 0 : 1 -4.04957e-17 -1.7257e-16 3.03671e-17 1.81076e-16 1 : -4.04957e-17 1 -3.28559e-17 -2.72704e-17 2.9934e-17 2 : -1.7257e-16 -3.28559e-17 1 -1.92834e-16 -3.04566e-16 3 : 3.03671e-17 -2.72704e-17 -1.92834e-16 1 -4.74819e-17 4 : 1.81076e-16 2.9934e-17 -3.04566e-16 -4.74819e-17 1 R8NSYMM_GEN_TEST R8NSYMM_GEN makes 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 2 -1.28978 2 -1.28978 3 -0.74152 3 -0.74152 4 -0.193259 4 -0.193259 13 0.355001 5 0.355001 24 0.903262 6 0.903262 19 1.45152 7 1.45152 17 1.99978 8 1.99978 12 2.54804 9 2.54804 2 3.0963 10 3.0963 3 3.64456 11 3.64456 1 LAMBDA versus column norms of A*QR: 0: 2.67904 2.67904 1: 0.43394 0.43394 2: 2.21293 2.21293 3: 2.26938 2.26938 4: -0.666087 0.666087 5: -1.24246 1.24246 6: 1.03967 1.03967 7: 1.67307 1.67307 8: 0.724873 0.724873 9: 3.164 3.164 10: 1.29779 1.29779 11: 3.04454 3.04454 12: 2.39882 2.39882 13: -0.242985 0.242985 14: 0.932916 0.932916 15: 0.205604 0.205604 16: 0.476232 0.476232 17: 0.649433 0.649433 18: 1.1317 1.1317 19: 1.53738 1.53738 20: 0.293584 0.293584 21: 0.366553 0.366553 22: 0.610616 0.610616 23: 0.369065 0.369065 24: 1.28042 1.28042 25: 0.42451 0.42451 26: 1.38554 1.38554 27: 0.72368 0.72368 28: 1.03913 1.03913 29: 0.384708 0.384708 30: 0.671167 0.671167 31: -1.83804 1.83804 32: -0.710951 0.710951 33: 2.01779 2.01779 34: 3.64456 3.64456 35: 2.46052 2.46052 36: 2.05497 2.05497 37: 1.40995 1.40995 38: 1.36145 1.36145 39: 1.22203 1.22203 40: 0.87868 0.87868 41: 1.77779 1.77779 42: 1.28288 1.28288 43: 2.12355 2.12355 44: 0.682151 0.682151 45: 0.77659 0.77659 46: 1.73471 1.73471 47: 1.58892 1.58892 48: 0.254638 0.254638 49: 0.231283 0.231283 50: 1.54825 1.54825 51: 0.597531 0.597531 52: 0.537876 0.537876 53: 0.180041 0.180041 54: 2.16269 2.16269 55: 1.63257 1.63257 56: 0.48852 0.48852 57: 1.28193 1.28193 58: 2.08256 2.08256 59: 1.83468 1.83468 60: 1.67428 1.67428 61: 3.13233 3.13233 62: 0.698019 0.698019 63: 0.914097 0.914097 64: -1.2943 1.2943 65: -1.1446 1.1446 66: 0.992036 0.992036 67: 1.81194 1.81194 68: 2.1405 2.1405 69: 1.37981 1.37981 70: 2.52867 2.52867 71: 1.71298 1.71298 72: 0.552931 0.552931 73: 1.13508 1.13508 74: 0.324614 0.324614 75: 3.33146 3.33146 76: 0.178454 0.178454 77: 0.0532788 0.0532788 78: 1.04643 1.04643 79: 0.402445 0.402445 80: 0.21364 0.21364 81: 0.381924 0.381924 82: 1.59603 1.59603 83: -0.662889 0.662889 84: 1.72675 1.72675 85: 1.49661 1.49661 86: -0.173372 0.173372 87: 0.158202 0.158202 88: 1.17585 1.17585 89: 0.60457 0.60457 90: 0.035255 0.035255 91: 2.11807 2.11807 92: 0.370307 0.370307 93: 0.063247 0.063247 94: 1.61747 1.61747 95: 0.904797 0.904797 96: -1.24479 1.24479 97: 1.89127 1.89127 98: 1.47777 1.47777 99: 0.847075 0.847075 R8SYMM_GEN_TEST R8SYMM_GEN makes 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 2 -1.28978 2 -1.28978 3 -0.74152 3 -0.74152 4 -0.193259 4 -0.193259 13 0.355001 5 0.355001 24 0.903262 6 0.903262 19 1.45152 7 1.45152 17 1.99978 8 1.99978 12 2.54804 9 2.54804 2 3.0963 10 3.0963 3 3.64456 11 3.64456 1 LAMBDA versus column norms of A*Q: 0: 2.67904 2.67904 1: 0.43394 0.43394 2: 2.21293 2.21293 3: 2.26938 2.26938 4: -0.666087 0.666087 5: -1.24246 1.24246 6: 1.03967 1.03967 7: 1.67307 1.67307 8: 0.724873 0.724873 9: 3.164 3.164 10: 1.29779 1.29779 11: 3.04454 3.04454 12: 2.39882 2.39882 13: -0.242985 0.242985 14: 0.932916 0.932916 15: 0.205604 0.205604 16: 0.476232 0.476232 17: 0.649433 0.649433 18: 1.1317 1.1317 19: 1.53738 1.53738 20: 0.293584 0.293584 21: 0.366553 0.366553 22: 0.610616 0.610616 23: 0.369065 0.369065 24: 1.28042 1.28042 25: 0.42451 0.42451 26: 1.38554 1.38554 27: 0.72368 0.72368 28: 1.03913 1.03913 29: 0.384708 0.384708 30: 0.671167 0.671167 31: -1.83804 1.83804 32: -0.710951 0.710951 33: 2.01779 2.01779 34: 3.64456 3.64456 35: 2.46052 2.46052 36: 2.05497 2.05497 37: 1.40995 1.40995 38: 1.36145 1.36145 39: 1.22203 1.22203 40: 0.87868 0.87868 41: 1.77779 1.77779 42: 1.28288 1.28288 43: 2.12355 2.12355 44: 0.682151 0.682151 45: 0.77659 0.77659 46: 1.73471 1.73471 47: 1.58892 1.58892 48: 0.254638 0.254638 49: 0.231283 0.231283 50: 1.54825 1.54825 51: 0.597531 0.597531 52: 0.537876 0.537876 53: 0.180041 0.180041 54: 2.16269 2.16269 55: 1.63257 1.63257 56: 0.48852 0.48852 57: 1.28193 1.28193 58: 2.08256 2.08256 59: 1.83468 1.83468 60: 1.67428 1.67428 61: 3.13233 3.13233 62: 0.698019 0.698019 63: 0.914097 0.914097 64: -1.2943 1.2943 65: -1.1446 1.1446 66: 0.992036 0.992036 67: 1.81194 1.81194 68: 2.1405 2.1405 69: 1.37981 1.37981 70: 2.52867 2.52867 71: 1.71298 1.71298 72: 0.552931 0.552931 73: 1.13508 1.13508 74: 0.324614 0.324614 75: 3.33146 3.33146 76: 0.178454 0.178454 77: 0.0532788 0.0532788 78: 1.04643 1.04643 79: 0.402445 0.402445 80: 0.21364 0.21364 81: 0.381924 0.381924 82: 1.59603 1.59603 83: -0.662889 0.662889 84: 1.72675 1.72675 85: 1.49661 1.49661 86: -0.173372 0.173372 87: 0.158202 0.158202 88: 1.17585 1.17585 89: 0.60457 0.60457 90: 0.035255 0.035255 91: 2.11807 2.11807 92: 0.370307 0.370307 93: 0.063247 0.063247 94: 1.61747 1.61747 95: 0.904797 0.904797 96: -1.24479 1.24479 97: 1.89127 1.89127 98: 1.47777 1.47777 99: 0.847075 0.847075 TEST_EIGEN_TEST Normal end of execution. Thu Sep 13 18:51:45 2018