Tue May 20 22:34:13 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 : 4.45638 2.17465 0.482285 4.77501 1 : 4.15461 4.61529 4.45352 1.81414 2 : 1.47792 0.195475 2.44036 2.45548 3 : 2.48335 4.6188 3.2943 0.813025 Working on column K = 0 Householder matrix H: Col: 0 1 2 3 Row 0 : -0.660866 -0.616114 -0.21917 -0.368272 1 : -0.616114 0.771447 -0.0813031 -0.136614 2 : -0.21917 -0.0813031 0.971078 -0.0485976 3 : -0.368272 -0.136614 -0.0485976 0.918341 Product H*A: Col: 0 1 2 3 Row 0 : -6.74325 -6.02451 -4.81065 -5.11094 1 : -4.9785e-17 1.57373 2.49005 -1.85314 2 :-2.37414e-16 -0.886496 1.7419 1.15092 3 :-5.77267e-16 2.80076 2.12067 -1.37903 Working on column K = 1 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 -0.472212 0.266001 -0.840393 2 : 0 0.266001 0.951939 0.151843 3 : 0 -0.840393 0.151843 0.520273 Product H*A: Col: 0 1 2 3 Row 0 : -6.74325 -6.02451 -4.81065 -5.11094 1 : 4.45488e-16 -3.33268 -2.49468 2.34015 2 :-3.26901e-16 3.12915e-17 2.64255 0.393267 3 :-2.94547e-16 3.54854e-16 -0.7248 1.01465 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 -0.964383 0.264512 3 : 0 0 0.264512 0.964383 Product H*A: Col: 0 1 2 3 Row 0 : -6.74325 -6.02451 -4.81065 -5.11094 1 : 4.45488e-16 -3.33268 -2.49468 2.34015 2 : 2.37346e-16 6.3686e-17 -2.74014 -0.110872 3 :-3.70525e-16 3.50492e-16 3.16067e-17 1.08254 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 : -2.00079 -4.32714 -1.36576 2.01212 3.39137 1 : -4.06134 2.86377 4.59615 -3.51497 -2.45182 2 : 0.164554 -1.63837 4.88976 -0.357147 -4.98998 3 : 0.78344 -1.51153 -1.10802 -0.171032 -1.95425 4 : -1.74786 -2.94962 -4.25724 -1.19906 -4.65175 Compact vector V so column 3 of H*A is packed: 0: 0 1: 0 2: 0.933655 3: -0.090215 4: -0.346626 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 -0.743424 0.168459 0.647257 3 : 0 0 0.168459 0.983723 -0.0625416 4 : 0 0 0.647257 -0.0625416 0.759701 Indirect product A*H: Col: 0 1 2 3 4 Row 0 : -2.00079 -4.32714 3.54939 1.53719 1.56659 1 : -4.06134 2.86377 -5.59598 -2.53015 1.33207 2 : 0.164554 -1.63837 -6.92513 0.784473 -0.603624 3 : 0.78344 -1.51153 -0.469991 -0.232681 -2.19112 4 : -1.74786 -2.94962 -0.0479393 -1.60578 -6.21448 Direct product A*H: Col: 0 1 2 3 4 Row 0 : -2.00079 -4.32714 3.54939 1.53719 1.56659 1 : -4.06134 2.86377 -5.59598 -2.53015 1.33207 2 : 0.164554 -1.63837 -6.92513 0.784473 -0.603624 3 : 0.78344 -1.51153 -0.469991 -0.232681 -2.19112 4 : -1.74786 -2.94962 -0.0479393 -1.60578 -6.21448 H*A should pack column 3: Col: 0 1 2 3 4 Row 0 : -2.00079 -4.32714 -1.36576 2.01212 3.39137 1 : -4.06134 2.86377 4.59615 -3.51497 -2.45182 2 : -1.12167 -0.945791 -6.57735 -0.539399 0.369577 3 : 0.907723 -1.57845 -8.35094e-17 -0.153421 -2.47212 4 : -1.27034 -3.20675 -5.79488e-16 -1.13139 -6.64152 r8mat_orth_uniform_test(): r8mat_orth_uniform() generates a random orthogopnal matrix. The matrix Q: Col: 0 1 2 3 4 Row 0 : -0.951196 0.231412 0.134442 -0.133462 -0.076075 1 : 0.0592516 -0.465576 0.803772 -0.329128 -0.159228 2 : 0.0422926 -0.0957405 -0.425743 -0.89876 0.00431777 3 : 0.14216 0.287579 -0.0360563 -0.0114116 -0.946392 4 : 0.26404 0.798636 0.39156 -0.256833 0.270522 The matrix Q'Q: Col: 0 1 2 3 4 Row 0 : 1 2.2317e-17 4.19279e-17 -3.58252e-17 -6.67784e-17 1 : 2.2317e-17 1 1.04492e-16 -1.25457e-16 -1.50982e-16 2 : 4.19279e-17 1.04492e-16 1 -5.83156e-17 2.84174e-17 3 :-3.58252e-17 -1.25457e-16 -5.83156e-17 1 1.27246e-17 4 :-6.67784e-17 -1.50982e-16 2.84174e-17 1.27246e-17 1 r8nsymm_gen_test(): r8nsymm_gen() generates an arbitrary size nonsymmetric matrix with known eigenvalues and eigenvectors. LAMDA_MIN = 0.41491357435184995 LAMDA_MAX = 13.84339024836278 Lamda bins: Index Lower Limit Count Upper Limit 0 0 0.414914 1 0.414914 1 1.75776 2 1.75776 0 3.10061 3 3.10061 2 4.44346 4 4.44346 0 5.7863 5 5.7863 0 7.12915 6 7.12915 0 8.472 7 8.472 1 9.81485 8 9.81485 0 11.1577 9 11.1577 0 12.5005 10 12.5005 0 13.8434 11 13.8434 1 The matrix A: [[ 14.32792053 1.8482699 1.1028086 8.23921007 -3.71360155] [ 10.39338932 2.77878968 15.68986064 8.97272623 4.96020616] [ 0.34513176 5.57014042 6.59104219 2.47759658 -1.33976717] [ -0.09614925 -11.27220441 1.48053791 2.85489794 1.92741491] [ -8.56525025 -5.54870149 -8.43350189 -8.69419532 4.50071335]] The matrix Q: [[-0.36307622 -0.02787098 -0.32898751 0.7253185 0.48278272] [-0.08630015 -0.91404798 0.18460508 -0.19055506 0.29441181] [ 0.34865683 -0.03298354 -0.81529589 -0.37508464 0.26824361] [-0.47575682 -0.27754203 -0.43761926 0.02544823 -0.71025885] [-0.71611578 0.29261238 0.03834292 -0.54430298 0.32221152]] The matrix T: [[ 3.94755035 14.73483779 5.63754906 7.15752597 7.91169079] [ 0. 0.41491357 11.87239755 15.77881736 13.64715007] [ 0. 0. 8.66281081 2.82926776 -0.60816674] [ 0. 0. 0. 4.1846987 2.48597749] [ 0. 0. 0. 0. 13.84339025]] The eigenvalues LAMDA (sorted): [ 0.41491357 3.94755035 4.1846987 8.66281081 13.84339025] Q * T * Q should equal A [[ 14.32792053 1.8482699 1.1028086 8.23921007 -3.71360155] [ 10.39338932 2.77878968 15.68986064 8.97272623 4.96020616] [ 0.34513176 5.57014042 6.59104219 2.47759658 -1.33976717] [ -0.09614925 -11.27220441 1.48053791 2.85489794 1.92741491] [ -8.56525025 -5.54870149 -8.43350189 -8.69419532 4.50071335]] r8symm_gen_test(): r8symm_gen() makes an arbitrary size symmetric matrix with known eigenvalues and eigenvectors. what9 LAMDA_MIN = 2.568 LAMDA_MAX = 14.8448 Lamda bins: Index Lower Limit Count Upper Limit 0 0 2.568 1 2.568 1 3.79569 2 3.79569 0 5.02337 3 5.02337 1 6.25105 4 6.25105 3 7.47873 5 7.47873 1 8.70641 6 8.70641 0 9.93409 7 9.93409 2 11.1618 8 11.1618 1 12.3894 9 12.3894 0 13.6171 10 13.6171 0 14.8448 11 14.8448 1 LAMDA versus column norms of A*Q: 0: 5.28991 5.28991 1: 6.82803 6.82803 2: 7.0156 7.0156 3: 11.5308 11.5308 4: 8.58804 8.58804 5: 7.17237 7.17237 6: 11.1389 11.1389 7: 2.568 2.568 8: 14.8448 14.8448 9: 10.7026 10.7026 test_eigen_test(): Normal end of execution. Tue May 20 22:34:14 2025