Wed Oct 8 07:27:28 2025 cg_test(): python version: 3.10.12 numpy version: 1.26.4 Test cg(). orth_random_test() orth_random() computes a random orthogal matrix. ORTH_RANDOM matrix: Col: 0 1 2 3 4 Row 0 : -0.127775 -0.214159 -0.807809 -0.0865765 -0.527029 1 : 0.295598 -0.484327 0.233789 -0.782587 -0.104643 2 : 0.0542725 -0.813526 -0.0697447 0.456426 0.349344 3 : 0.906513 0.114022 -0.0277633 0.30003 -0.272844 4 : 0.267552 0.211514 -0.535866 -0.285867 0.7175 spd_random_test(): spd_random() computes the spd_random matrix. spd_random matrix: Col: 0 1 2 3 4 Row 0 : 0.841507 0.0124888 0.0371599 0.0918867 0.0559793 1 : 0.0124888 0.654655 0.0912092 -0.172516 -0.120682 2 : 0.0371599 0.0912092 0.831126 -0.0708292 -0.00601272 3 : 0.0918867 -0.172516 -0.0708292 0.150357 -0.16669 4 : 0.0559793 -0.120682 -0.00601272 -0.16669 0.753773 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 : 2.73142 3.28992 3.35494 -3.76749 -2.78655 1 : -3.69824 -4.94151 0.914406 4.72599 2.48305 2 : 4.44872 -2.22717 2.85492 -2.96377 2.74379 3 : -0.969025 -0.750968 4.76507 2.1819 -3.09691 4 : 1.51795 -2.98697 -0.102557 2.43145 -0.515408 Compact vector V so column 3 of H*A is packed: 0: 0 1: 0 2: 0.870018 3: 0.492906 4: -0.0106087 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 -0.513862 -0.857674 0.0184595 3 : 0 0 -0.857674 0.514087 0.0104582 4 : 0 0 0.0184595 0.0104582 0.999775 Indirect product A*H: Col: 0 1 2 3 4 Row 0 : 2.73142 3.28992 1.45586 -4.84341 -2.76339 1 : -3.69824 -4.94151 -4.4774 1.67128 2.5488 2 : 4.44872 -2.22717 1.12556 -3.94353 2.76487 3 : -0.969025 -0.750968 -4.37712 -2.99758 -2.98544 4 : 1.51795 -2.98697 -2.04221 1.33255 -0.491757 Direct product A*H: Col: 0 1 2 3 4 Row 0 : 2.73142 3.28992 1.45586 -4.84341 -2.76339 1 : -3.69824 -4.94151 -4.4774 1.67128 2.5488 2 : 4.44872 -2.22717 1.12556 -3.94353 2.76487 3 : -0.969025 -0.750968 -4.37712 -2.99758 -2.98544 4 : 1.51795 -2.98697 -2.04221 1.33255 -0.491757 H*A should pack column 3: Col: 0 1 2 3 4 Row 0 : 2.73142 3.28992 3.35494 -3.76749 -2.78655 1 : -3.69824 -4.94151 0.914406 4.72599 2.48305 2 : -1.4269 1.7334 -5.5558 -0.30351 1.2367 3 : -4.29784 1.49288 -4.26742e-16 3.68907 -3.95075 4 : 1.58959 -3.03526 0 2.39901 -0.497031 r8mat_house_form_test(): Python version: 3.10.12 r8mat_house_form() forms a Householder matrix from its compact form. Compact vector form V: 0: 0 1: 0 2: 1 3: 2 4: 3 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 0.857143 -0.285714 -0.428571 3 : 0 0 -0.285714 0.428571 -0.857143 4 : 0 0 -0.428571 -0.857143 -0.285714 r8mat_mm_test(): Python version: 3.10.12 r8mat_mm() computes a matrix-matrix product C = A * B; A: Col: 0 1 2 Row 0 : 1 0 0 1 : 1 1 0 2 : 1 2 1 3 : 1 3 3 B: Col: 0 1 2 3 Row 0 : 1 1 1 1 1 : 0 1 2 3 2 : 0 0 1 3 C = A*B: Col: 0 1 2 3 Row 0 : 1 1 1 1 1 : 1 2 3 4 2 : 1 3 6 10 3 : 1 4 10 19 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 : 1.35137 4.69802 2.25227 0.792036 1 : 3.31181 0.309316 2.39387 1.18724 2 : 1.45169 0.558404 3.24526 1.76919 3 : 4.872 3.27951 4.97459 2.02626 Working on column K = 0 Householder matrix H: Col: 0 1 2 3 Row 0 : -0.217404 -0.532792 -0.233542 -0.78379 1 : -0.532792 0.766825 -0.102209 -0.343023 2 : -0.233542 -0.102209 0.955198 -0.150359 3 : -0.78379 -0.343023 -0.150359 0.49538 Product H*A: Col: 0 1 2 3 Row 0 : -6.21595 -3.88702 -6.42202 -2.80609 1 : 2.22045e-16 -3.4479 -1.4024 -0.387465 2 : 1.11022e-16 -1.08852 1.58121 1.07894 3 : 1.33227e-15 -2.24772 -0.610095 -0.290284 Working on column K = 1 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 -0.809867 -0.255679 -0.527961 2 : 0 -0.255679 0.96388 -0.0745849 3 : 0 -0.527961 -0.0745849 0.845987 Product H*A: Col: 0 1 2 3 Row 0 : -6.21595 -3.88702 -6.42202 -2.80609 1 :-9.11598e-16 4.25736 1.05358 0.191192 2 : -4.9127e-17 -5.55112e-17 1.92817 1.16068 3 : 1.00157e-15 -2.22045e-16 0.106346 -0.121482 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 -0.998482 -0.05507 3 : 0 0 -0.05507 0.998482 Product H*A: Col: 0 1 2 3 Row 0 : -6.21595 -3.88702 -6.42202 -2.80609 1 :-9.11598e-16 4.25736 1.05358 0.191192 2 :-6.10399e-18 6.76549e-17 -1.9311 -1.15223 3 : 1.00276e-15 -2.18651e-16 0 -0.185217 r83_cg_test(): r83_cg() applies CG to an R83 matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 1.61556e-15 Norm of error ||x1-x2|| = 8.17973e-16 r83s_cg_test(): r83s_cg() applies CG to an R83S matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 8.61121e-15 Norm of error ||x1-x2|| = 2.31748e-15 r83t_cg_test(): r83t_cg() applies CG to an R83T matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 6.63352e-15 Norm of error ||x1-x2|| = 2.07315e-15 r8ge_cg_test(): r8ge_cg() applies CG to an R8GE matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 2.59566e-16 Norm of error ||x1-x2|| = 1.21716e-15 r8pbu_cg_test(): r8pbu_cg() applies CG to an R8PBU matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 4.83935e-16 Norm of error ||x1-x2|| = 8.71432e-16 r8sd_cg_test(): r8sd_cg() applies CG to an R8SD matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 1.32879e-15 Norm of error ||x1-x2|| = 1.40104e-15 cg_test(): Normal end of execution. Wed Oct 8 07:27:28 2025