Tue Jun 4 17:54:33 2024 test_eigen_test(): python version: 3.10.12 numpy version: 1.26.4 Test test_eigen(). r8vec_house_column_test(): 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 : 3.16881 4.80322 4.57189 0.359459 1 : 3.20231 2.96615 1.40418 4.27093 2 : 3.93882 2.50293 0.593444 3.79056 3 : 2.50026 1.70298 0.75822 3.43298 Working on column K = 0 Householder matrix H: Col: 0 1 2 3 Row 0 : -0.488599 -0.493764 -0.607326 -0.385515 1 : -0.493764 0.83622 -0.201449 -0.127874 2 : -0.607326 -0.201449 0.75222 -0.157284 3 : -0.385515 -0.127874 -0.157284 0.90016 Product H*A: Col: 0 1 2 3 Row 0 : -6.4855 -5.98804 -3.57988 -5.91004 1 : 5.81803e-16 -0.613285 -1.29973 2.19135 2 : 2.48216e-16 -1.89975 -2.73235 1.2327 3 : 3.40869e-16 -1.09173 -1.35291 1.80931 Working on column K = 1 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 -0.269539 -0.834941 -0.479815 2 : 0 -0.834941 0.450882 -0.315561 3 : 0 -0.479815 -0.315561 0.818657 Product H*A: Col: 0 1 2 3 Row 0 : -6.4855 -5.98804 -3.57988 -5.91004 1 :-5.27619e-16 2.27531 3.28083 -2.48802 2 : -4.8142e-16 -2.60002e-16 0.280156 -1.8448 3 :-7.84306e-17 -9.89419e-19 0.378286 0.0407683 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 -0.59515 -0.803614 3 : 0 0 -0.803614 0.59515 Product H*A: Col: 0 1 2 3 Row 0 : -6.4855 -5.98804 -3.57988 -5.91004 1 :-5.27619e-16 2.27531 3.28083 -2.48802 2 : 3.49545e-16 1.55535e-16 -0.470731 1.06517 3 : 3.40198e-16 2.08352e-16 1.71984e-17 1.50677 r8mat_house_axh_test(): r8mat_house_axh() multiplies a matrix A times a compact Householder matrix. Matrix A: Col: 0 1 2 3 4 Row 0 : -3.74217 2.33271 -4.7379 1.80368 -4.28513 1 : 2.55675 -0.349655 4.71999 -2.76215 1.37465 2 : -1.98569 -3.07474 -3.48984 1.81209 -3.9745 3 : -4.29396 2.99333 -2.29874 -1.30776 1.78813 4 : 0.561907 -0.790974 -1.40758 -1.25066 -2.14744 Compact vector V so column 3 of H*A is packed: 0: 0 1: 0 2: -0.94642 3: -0.275409 4: -0.168641 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 -0.79142 -0.521306 -0.31921 3 : 0 0 -0.521306 0.848299 -0.0928905 4 : 0 0 -0.31921 -0.0928905 0.943121 Indirect product A*H: Col: 0 1 2 3 4 Row 0 : -3.74217 2.33271 4.17726 4.398 -2.69656 1 : 2.55675 -0.349655 -2.73437 -4.93138 0.0463715 2 : -1.98569 -3.07474 3.08597 3.72566 -2.80277 3 : -4.29396 2.99333 1.93023 -0.0771272 2.54169 4 : 0.561907 -0.790974 2.45145 -0.127674 -1.4598 Direct product A*H: Col: 0 1 2 3 4 Row 0 : -3.74217 2.33271 4.17726 4.398 -2.69656 1 : 2.55675 -0.349655 -2.73437 -4.93138 0.0463715 2 : -1.98569 -3.07474 3.08597 3.72566 -2.80277 3 : -4.29396 2.99333 1.93023 -0.0771272 2.54169 4 : 0.561907 -0.790974 2.45145 -0.127674 -1.4598 H*A should pack column 3: Col: 0 1 2 3 4 Row 0 : -3.74217 2.33271 -4.7379 1.80368 -4.28513 1 : 2.55675 -0.349655 4.71999 -2.76215 1.37465 2 : 3.63061 1.12546 4.40959 -0.353158 2.89882 3 : -2.65961 4.21559 1.18015e-16 -1.93785 3.78828 4 : 1.56267 -0.0425489 7.47962e-17 -1.63648 -0.922693 r8mat_orth_uniform_test(): r8mat_orth_uniform() generates a random orthogopnal matrix. The matrix Q: Col: 0 1 2 3 4 Row 0 : -0.139273 -0.328986 -0.722499 0.0787274 0.586659 1 : -0.218696 -0.228167 0.0640787 -0.946218 0.0260251 2 : 0.875198 -0.0782067 0.18316 -0.159717 0.41092 3 : 0.406653 0.0180433 -0.627347 -0.158555 -0.644674 4 : -0.037914 0.912834 -0.21628 -0.218688 0.265885 The matrix Q'Q: Col: 0 1 2 3 4 Row 0 : 1 2.9302e-17 -2.05026e-16 8.34516e-17 8.06887e-17 1 : 2.9302e-17 1 -1.46295e-16 4.32308e-16 -2.86562e-17 2 :-2.05026e-16 -1.46295e-16 1 -5.39256e-17 2.43389e-16 3 : 8.34516e-17 4.32308e-16 -5.39256e-17 1 2.77361e-16 4 : 8.06887e-17 -2.86562e-17 2.43389e-16 2.77361e-16 1 r8nsymm_gen_test(): r8nsymm_gen() generates an arbitrary size nonsymmetric matrix with known eigenvalues and eigenvectors. LAMDA_MIN = 2.708904957478957 LAMDA_MAX = 18.62784690911463 Lamda bins: Index Lower Limit Count Upper Limit 0 0 2.7089 1 2.7089 2 4.3008 2 4.3008 0 5.89269 3 5.89269 0 7.48459 4 7.48459 0 9.07648 5 9.07648 0 10.6684 6 10.6684 0 12.2603 7 12.2603 1 13.8522 8 13.8522 0 15.4441 9 15.4441 1 17.036 10 17.036 0 18.6278 11 18.6278 1 The matrix A: [[ 3.58645787 -2.0912464 5.25975918 -5.27342065 -1.80390231] [ 0.15902333 19.69750136 -8.67698482 11.46944808 12.8111215 ] [ 6.81722039 -6.4928903 19.26197956 -12.01381171 -18.19224671] [-14.7930814 2.03088634 6.86141337 11.08114159 11.42851449] [ -0.86010682 -4.58878333 1.99571881 -4.23863276 2.35362982]] The matrix Q: [[-0.61537671 0.41886182 -0.3569243 -0.27377087 -0.4934783 ] [ 0.08984915 -0.09956246 -0.189997 0.82418361 -0.51636902] [ 0.50712786 0.71273136 -0.41842747 0.0792364 0.23124745] [-0.21408698 -0.43822911 -0.76477113 0.05556251 0.41732474] [-0.55698002 0.33854297 0.27667626 0.48621527 0.5120614 ]] The matrix T: [[ 4.26796486 6.70657341 19.47653985 11.03508087 10.03642687] [ 0. 2.70890496 -1.87890251 4.52839815 19.85350334] [ 0. 0. 18.62784691 9.88154695 17.27641194] [ 0. 0. 0. 16.5682527 6.61595242] [ 0. 0. 0. 0. 13.80774077]] The eigenvalues LAMDA (sorted): [ 2.70890496 4.26796486 13.80774077 16.5682527 18.62784691] Q * T * Q should equal A [[ 3.58645787 -2.0912464 5.25975918 -5.27342065 -1.80390231] [ 0.15902333 19.69750136 -8.67698482 11.46944808 12.8111215 ] [ 6.81722039 -6.4928903 19.26197956 -12.01381171 -18.19224671] [-14.7930814 2.03088634 6.86141337 11.08114159 11.42851449] [ -0.86010682 -4.58878333 1.99571881 -4.23863276 2.35362982]] r8symm_gen_test(): r8symm_gen() makes an arbitrary size symmetric matrix with known eigenvalues and eigenvectors. what9 LAMDA_MIN = -0.993149 LAMDA_MAX = 14.9493 Lamda bins: Index Lower Limit Count Upper Limit 0 0 -0.993149 1 -0.993149 2 0.601101 2 0.601101 1 2.19535 3 2.19535 0 3.7896 4 3.7896 1 5.38385 5 5.38385 0 6.9781 6 6.9781 0 8.57235 7 8.57235 2 10.1666 8 10.1666 2 11.7608 9 11.7608 0 13.3551 10 13.3551 1 14.9493 11 14.9493 1 LAMDA versus column norms of A*Q: 0: 10.5365 10.5365 1: 14.9493 14.9493 2: 8.79477 8.79477 3: 14.724 14.724 4: 11.6485 11.6485 5: 9.43974 9.43974 6: 5.05135 5.05135 7: 1.94475 1.94475 8: -0.993149 0.993149 9: 0.329774 0.329774 test_eigen_test(): Normal end of execution. Tue Jun 4 17:54:33 2024