Wed Oct 8 08:57:55 2025 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 : 3.74881 2.1338 1.92216 1.12448 1 : 1.81753 1.36904 4.47743 1.42223 2 : 1.65091 1.64035 0.596857 3.59955 3 : 2.17746 4.5471 2.8207 1.7185 Working on column K = 0 Householder matrix H: Col: 0 1 2 3 Row 0 : -0.752418 -0.364793 -0.331352 -0.437035 1 : -0.364793 0.924063 -0.0689761 -0.0909756 2 : -0.331352 -0.0689761 0.937347 -0.0826358 3 : -0.437035 -0.0909756 -0.0826358 0.891008 Product H*A: Col: 0 1 2 3 Row 0 : -4.98235 -4.63571 -4.51011 -3.30866 1 :-4.57349e-16 -0.0401347 3.13845 0.499399 2 :-1.57206e-17 0.360356 -0.619374 2.76132 3 :-1.65171e-16 2.85886 1.21656 0.612921 Working on column K = 1 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 -0.0139272 0.125047 0.992053 2 : 0 0.125047 0.984578 -0.122349 3 : 0 0.992053 -0.122349 0.0293492 Product H*A: Col: 0 1 2 3 Row 0 : -4.98235 -4.63571 -4.51011 -3.30866 1 :-1.59455e-16 2.88176 1.08573 0.94639 2 :-5.24598e-17 -2.89319e-17 -0.366213 2.70619 3 :-4.56639e-16 -6.29564e-16 3.225 0.175574 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 -0.112829 0.993614 3 : 0 0 0.993614 0.112829 Product H*A: Col: 0 1 2 3 Row 0 : -4.98235 -4.63571 -4.51011 -3.30866 1 :-1.59455e-16 2.88176 1.08573 0.94639 2 :-4.47804e-16 -6.2228e-16 3.24572 -0.130885 3 :-1.03647e-16 -9.97804e-17 4.64764e-16 2.70872 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 : -2.44838 1.99331 0.221027 0.045018 -4.74358 1 : 2.86207 -2.53844 -1.66423 -4.01414 -0.344917 2 : 0.347458 -4.65735 -4.61598 2.26125 -1.14715 3 : 0.851688 -1.18876 2.86045 -1.35347 -3.01554 4 : 4.83799 2.7394 0.711785 -1.3914 -2.11176 Compact vector V so column 3 of H*A is packed: 0: 0 1: 0 2: -0.959899 3: 0.272048 4: 0.0676957 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 -0.842814 0.522278 0.129962 3 : 0 0 0.522278 0.851979 -0.036833 4 : 0 0 0.129962 -0.036833 0.990835 Indirect product A*H: Col: 0 1 2 3 4 Row 0 : -2.44838 1.99331 -0.779259 0.328513 -4.67303 1 : 2.86207 -2.53844 -0.738688 -4.27646 -0.41019 2 : 0.347458 -4.65735 4.92232 -0.442038 -1.81982 3 : 0.851688 -1.18876 -3.50962 0.451893 -2.5663 4 : 4.83799 2.7394 -1.60105 -0.735912 -1.94865 Direct product A*H: Col: 0 1 2 3 4 Row 0 : -2.44838 1.99331 -0.779259 0.328513 -4.67303 1 : 2.86207 -2.53844 -0.738688 -4.27646 -0.41019 2 : 0.347458 -4.65735 4.92232 -0.442038 -1.81982 3 : 0.851688 -1.18876 -3.50962 0.451893 -2.5663 4 : 4.83799 2.7394 -1.60105 -0.735912 -1.94865 H*A should pack column 3: Col: 0 1 2 3 4 Row 0 : -2.44838 1.99331 0.221027 0.045018 -4.74358 1 : 2.86207 -2.53844 -1.66423 -4.01414 -0.344917 2 : 0.780732 3.66044 5.47686 -2.79353 -0.882568 3 : 0.728893 -3.54613 -4.64203e-16 0.0791203 -3.09052 4 : 4.80743 2.1528 -2.37427e-17 -1.03492 -2.13042 r8mat_orth_uniform_test(): r8mat_orth_uniform() generates a random orthogopnal matrix. The matrix Q: Col: 0 1 2 3 4 Row 0 : -0.117604 0.347357 -0.929507 0.0100252 -0.0378037 1 : -0.892031 -0.414827 -0.0463601 -0.162559 0.0602096 2 : 0.315221 -0.287934 -0.170109 -0.821081 0.338554 3 : 0.0255217 -0.0507453 0.0118225 -0.358959 -0.931548 4 : -0.300724 0.788531 0.323714 -0.412855 0.112002 The matrix Q'Q: Col: 0 1 2 3 4 Row 0 : 1 5.25265e-18 1.13522e-16 9.35624e-18 -3.22245e-17 1 : 5.25265e-18 1 -5.26367e-17 1.13273e-16 -3.83238e-17 2 : 1.13522e-16 -5.26367e-17 1 1.33334e-16 -1.51734e-17 3 : 9.35624e-18 1.13273e-16 1.33334e-16 1 1.79597e-16 4 :-3.22245e-17 -3.83238e-17 -1.51734e-17 1.79597e-16 1 r8nsymm_gen_test(): r8nsymm_gen() generates an arbitrary size nonsymmetric matrix with known eigenvalues and eigenvectors. LAMDA_MIN = -0.2651400279164662 LAMDA_MAX = 14.778576202120771 Lamda bins: Index Lower Limit Count Upper Limit 0 0 -0.26514 1 -0.26514 1 1.23923 2 1.23923 0 2.7436 3 2.7436 0 4.24797 4 4.24797 0 5.75235 5 5.75235 0 7.25672 6 7.25672 0 8.76109 7 8.76109 0 10.2655 8 10.2655 2 11.7698 9 11.7698 0 13.2742 10 13.2742 1 14.7786 11 14.7786 1 The matrix A: [[ 6.8090744 -3.81165255 -6.88339439 -3.79808987 -14.30167483] [ -2.56051361 8.40519655 1.49710267 4.54776376 -11.93408681] [ -2.18913668 5.95435188 12.41040443 13.62717051 12.40979839] [ 3.37245006 -0.23663544 -5.23352118 -1.51905794 10.56118478] [ -1.33026561 9.74964436 -0.73984924 6.5463438 22.90968485]] The matrix Q: [[-0.86814248 -0.07292746 0.3749204 -0.28579239 0.13699498] [ 0.37246909 0.00601339 0.90572715 0.12961568 0.15520543] [-0.23756316 -0.49302148 -0.02668138 0.83518332 0.04743943] [ 0.15390206 -0.31862368 -0.18566381 -0.20104469 0.89437301] [-0.16575078 0.80625939 -0.06253059 0.40444078 0.39368778]] The matrix T: [[10.46808588 11.98598262 7.09977856 8.84747959 16.5486088 ] [ 0. 10.66483862 7.23648534 4.15998215 12.81900719] [ 0. 0. -0.26514003 19.48989479 3.65490495] [ 0. 0. 0. 14.7785762 11.29409979] [ 0. 0. 0. 0. 13.36894161]] The eigenvalues LAMDA (sorted): [-0.26514003 10.46808588 10.66483862 13.36894161 14.7785762 ] Q * T * Q should equal A [[ 6.8090744 -3.81165255 -6.88339439 -3.79808987 -14.30167483] [ -2.56051361 8.40519655 1.49710267 4.54776376 -11.93408681] [ -2.18913668 5.95435188 12.41040443 13.62717051 12.40979839] [ 3.37245006 -0.23663544 -5.23352118 -1.51905794 10.56118478] [ -1.33026561 9.74964436 -0.73984924 6.5463438 22.90968485]] r8symm_gen_test(): r8symm_gen() makes an arbitrary size symmetric matrix with known eigenvalues and eigenvectors. what9 LAMDA_MIN = 2.69713 LAMDA_MAX = 9.14281 Lamda bins: Index Lower Limit Count Upper Limit 0 0 2.69713 1 2.69713 1 3.3417 2 3.3417 1 3.98626 3 3.98626 1 4.63083 4 4.63083 0 5.2754 5 5.2754 2 5.91997 6 5.91997 0 6.56454 7 6.56454 0 7.2091 8 7.2091 2 7.85367 9 7.85367 2 8.49824 10 8.49824 0 9.14281 11 9.14281 1 LAMDA versus column norms of A*Q: 0: 8.48448 8.48448 1: 7.28513 7.28513 2: 4.52033 4.52033 3: 8.19674 8.19674 4: 5.82226 5.82226 5: 5.88084 5.88084 6: 3.8725 3.8725 7: 7.84076 7.84076 8: 9.14281 9.14281 9: 2.69713 2.69713 test_eigen_test(): Normal end of execution. Wed Oct 8 08:57:55 2025