Tue Oct 19 11:25:18 2021 cg_test(): Python version: 3.6.9 Test cg(). orth_random_test() Python version: 3.6.9 orth_random() computes a random orthogal matrix. ORTH_RANDOM matrix: Col: 0 1 2 3 4 Row 0 : -0.600864 -0.160632 0.404383 0.113381 -0.660893 1 : -0.577919 -0.434854 -0.319202 -0.502834 0.349543 2 : -0.500075 0.47782 -0.432241 0.553378 0.168977 3 : -0.0223691 0.625509 -0.242653 -0.631234 -0.388461 4 : -0.233232 0.406849 0.699193 -0.172103 0.511455 orth_random_test(): Normal end of execution. spd_random_test(): Python version: 3.6.9 spd_random() computes the spd_random matrix. spd_random matrix: Col: 0 1 2 3 4 Row 0 : 0.410905 0.0565127 0.0461125 -0.0815966 0.0830425 1 : 0.0565127 0.542703 -0.0700646 0.092661 -0.0287069 2 : 0.0461125 -0.0700646 0.57625 -0.0470775 -0.033762 3 : -0.0815966 0.092661 -0.0470775 0.562362 0.0787183 4 : 0.0830425 -0.0287069 -0.033762 0.0787183 0.454867 spd_random_test(): Normal end of execution. r8mat_house_axh_test() Python version: 3.6.9 r8mat_house_axh() multiplies a matrix A times a compact Householder matrix. Matrix A: Col: 0 1 2 3 4 Row 0 : -1.84632 -0.933446 4.80259 0.420652 -2.57705 1 : -2.47758 0.651558 -3.66663 3.76259 -0.196681 2 : -2.16674 3.92211 3.27632 4.7997 3.67233 3 : -3.06494 -0.455093 3.05183 2.47231 4.1996 4 : -2.7953 4.97953 1.02797 -4.64482 0.555211 Compact vector V so column 3 of H*A is packed: 0: 0 1: 0 2: 0.925521 3: 0.358885 4: 0.120885 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 -0.713177 -0.66431 -0.223764 3 : 0 0 -0.66431 0.742404 -0.0867677 4 : 0 0 -0.223764 -0.0867677 0.970774 Indirect product A*H: Col: 0 1 2 3 4 Row 0 : -1.84632 -0.933446 -3.12789 -2.65451 -3.61288 1 : -2.47758 0.651558 0.159442 5.2462 0.303054 2 : -2.16674 3.92211 -6.34682 1.06818 2.41542 3 : -3.06494 -0.455093 -4.75859 -0.556296 3.17945 4 : -2.7953 4.97953 2.22824 -4.17939 0.711983 Direct product A*H: Col: 0 1 2 3 4 Row 0 : -1.84632 -0.933446 -3.12789 -2.65451 -3.61288 1 : -2.47758 0.651558 0.159442 5.2462 0.303054 2 : -2.16674 3.92211 -6.34682 1.06818 2.41542 3 : -3.06494 -0.455093 -4.75859 -0.556296 3.17945 4 : -2.7953 4.97953 2.22824 -4.17939 0.711983 H*A should pack column 3: Col: 0 1 2 3 4 Row 0 : -1.84632 -0.933446 4.80259 0.420652 -2.57705 1 : -2.47758 0.651558 -3.66663 3.76259 -0.196681 2 : 4.20683 -3.60907 -4.59398 -4.02608 -5.53309 3 : -0.593494 -3.37542 -1.66533e-16 -0.950019 0.630054 4 : -1.96283 3.99586 0 -5.79758 -0.647139 r8mat_house_axh_test(): Normal end of execution. r8mat_house_form_test(): Python version: 3.6.9 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_house_form_test Normal end of execution. r8mat_mm_test(): Python version: 3.6.9 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 r8mat_mm_test(): Normal end of execution. r8mat_print_test(): Python version: 3.6.9 r8mat_print() prints an R8MAT. Here is an R8MAT: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 21 22 23 24 25 2 : 31 32 33 34 35 3 : 41 42 43 44 45 Col: 5 Row 0 : 16 1 : 26 2 : 36 3 : 46 r8mat_print_test(): Normal end of execution. r8mat_print_some_test(): Python version: 3.6.9 r8mat_print_some() prints some of an R8MAT. Here is an R8MAT: Col: 3 4 5 Row 0 : 14 15 16 1 : 24 25 26 2 : 34 35 36 r8mat_print_some_test(): Normal end of execution. r8vec_house_column_test(): Python version: 3.6.9 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 : 1.59821 2.51052 2.66561 3.31257 1 : 2.29138 0.549382 3.64969 3.92102 2 : 0.706449 4.19343 2.01363 2.03212 3 : 1.85333 4.58508 2.4534 4.82994 Working on column K = 0 Householder matrix H: Col: 0 1 2 3 Row 0 : -0.466473 -0.668788 -0.206192 -0.540935 1 : -0.668788 0.694998 -0.0940344 -0.246694 2 : -0.206192 -0.0940344 0.971009 -0.0760577 3 : -0.540935 -0.246694 -0.0760577 0.800467 Product H*A: Col: 0 1 2 3 Row 0 : -3.42616 -4.88339 -5.42662 -7.19924 1 :-3.88578e-16 -2.82263 -0.0407925 -0.872916 2 :-5.55112e-17 3.15382 0.87583 0.554114 3 : 0 1.8577 -0.531568 0.952473 Working on column K = 1 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 -0.610666 0.682318 0.401907 2 : 0 0.682318 0.710953 -0.170258 3 : 0 0.401907 -0.170258 0.899713 Product H*A: Col: 0 1 2 3 Row 0 : -3.42616 -4.88339 -5.42662 -7.19924 1 : 1.99415e-16 4.62221 0.408864 1.29395 2 : -3.046e-16 -3.88578e-16 0.685344 -0.363823 3 :-1.46721e-16 0 -0.64377 0.411779 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 -0.728868 0.684654 3 : 0 0 0.684654 0.728868 Product H*A: Col: 0 1 2 3 Row 0 : -3.42616 -4.88339 -5.42662 -7.19924 1 : 1.99415e-16 4.62221 0.408864 1.29395 2 : 1.2156e-16 2.83222e-16 -0.940285 0.547105 3 :-3.15486e-16 -2.66042e-16 -5.55112e-17 0.0510396 r8vec_house_column_test(): Normal end of execution. r8vec_print_test(): Python version: 3.6.9 r8vec_print() prints an R8VEC. Here is an R8VEC: 0: 123.456 1: 5e-06 2: -1e+06 3: 3.14159 r8vec_print_test(): Normal end of execution. r83_cg_test(): Python version: 3.6.9 r83_cg() applies CG to an R83 matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 2.69243e-15 Norm of error ||x1-x2|| = 8.98312e-16 r83_cg_test(): Normal end of execution. r83s_cg_test(): Python version: 3.6.9 r83s_cg() applies CG to an R83S matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 1.42833e-15 Norm of error ||x1-x2|| = 7.67932e-16 r83t_cg_test(): Python version: 3.6.9 r83t_cg() applies CG to an R83T matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 1.41472e-15 Norm of error ||x1-x2|| = 2.15356e-15 r8ge_cg_test(): Python version: 3.6.9 r8ge_cg() applies CG to an R8GE matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 3.52866e-16 Norm of error ||x1-x2|| = 5.95291e-16 r8ge_cg_test Normal end of execution. r8pbu_cg_test(): Python version: 3.6.9 r8pbu_cg() applies CG to an R8PBU matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 7.87006e-16 Norm of error ||x1-x2|| = 1.40613e-15 r8sd_cg_test(): Python version: 3.6.9 r8sd_cg() applies CG to an R8SD matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 4.07922e-16 Norm of error ||x1-x2|| = 1.05069e-15 cg_test(): Normal end of execution. Tue Oct 19 11:25:19 2021