Wed Oct 8 08:50:35 2025 r8sm_test(): python version: 3.10.12 numpy version: 1.26.4 Test r8sm(). r8sm_indicator_test(): r8sm_indicator() sets up an R8SM indicator matrix M = 5 N = 4 The R8SM indicator matrix: Col: 0 1 2 3 Row 0 : 11 12 13 14 1 : 21 22 23 24 2 : 31 32 33 34 3 : 41 42 43 44 4 : 51 52 53 54 R8SM_ML_TEST R8SM_ML computes A*x or A'*X where A is a Sherman Morrison matrix. Matrix rows M = 7 Matrix columns N = 7 The Sherman Morrison matrix: Col: 0 1 2 3 4 Row 0 : 0.205473 0.663829 0.486144 0.961996 0.272552 1 : 0.148034 0.666334 0.632728 0.809406 0.0118646 2 : 0.603934 0.376725 0.256407 0.560133 0.0739201 3 : 0.0311059 -0.00838633 0.0649779 -0.0352782 -0.0707253 4 : 0.546437 0.620136 0.161204 0.731463 0.522872 5 : 0.453363 0.344171 0.277198 0.701304 0.623826 6 : 0.288285 0.612903 0.702909 0.380775 0.0167069 Col: 5 6 Row 0 : 0.556236 0.423055 1 : -0.0338212 0.402705 2 : -0.103973 -0.160885 3 : 0.0930895 0.240838 4 : -0.709454 -0.0440548 5 : 0.252011 0.843081 6 : 0.320285 0.62015 A*x and PLU*x 0: 14.5011 14.5011 1: 9.29184 9.29184 2: 2.9867 2.9867 3: 1.95893 1.95893 4: 3.24543 3.24543 5: 15.3113 15.3113 6: 11.4922 11.4922 The Sherman Morrison matrix: Col: 0 1 2 3 4 Row 0 : 0.17618 0.0879559 0.0851015 -0.676443 0.347086 1 : -0.0484366 0.277665 0.571846 0.100281 0.734206 2 : 0.11845 -0.329121 -0.112345 0.0241998 -0.0713299 3 : -0.0320038 0.691886 0.127181 0.316193 0.747446 4 : 0.0626188 0.553679 0.0734978 0.953024 0.356291 5 : 0.0685186 0.0615626 0.856528 0.248395 0.636872 6 : -0.216812 0.276017 0.220042 0.192649 0.17503 Col: 5 6 Row 0 : 0.474749 -0.371554 1 : 0.109672 0.222706 2 : 0.520518 0.264929 3 : 0.276794 -0.124352 4 : 0.757755 0.164532 5 : -0.0813356 0.258456 6 : 0.631244 -0.304422 A'*x and (PLU)'*x 0: -0.486839 -0.486839 1: 7.49336 7.49336 2: 8.44743 8.44743 3: 8.46553 8.46553 4: 11.4192 11.4192 5: 11.0823 11.0823 6: 0.613677 0.613677 R8SM_MTV_TEST R8SM_MTV computes A'*x=b, where A is an R8SM matrix M = 5 N = 4 The R8SM matrix: Col: 0 1 2 3 Row 0 : 11 12 13 14 1 : 21 22 23 24 2 : 31 32 33 34 3 : 41 42 43 44 4 : 51 52 53 54 The vector x: 0: 1 1: 2 2: 3 3: 4 4: 5 The product b=A*x: 0: 565 1: 580 2: 595 3: 610 R8SM_MV_TEST R8SM_MV computes A*x=b, where A is an R8SM matrix M = 5 N = 4 The R8SM matrix: Col: 0 1 2 3 Row 0 : 11 12 13 14 1 : 21 22 23 24 2 : 31 32 33 34 3 : 41 42 43 44 4 : 51 52 53 54 The vector x: 0: 1 1: 2 2: 3 3: 4 The product b=A*x: 0: 130 1: 230 2: 330 3: 430 4: 530 R8SM_PRINT_TEST R8SM_PRINT prints an R8SM matrix M = 5 N = 4 The R8SM matrix: Col: 0 1 2 3 Row 0 : 11 12 13 14 1 : 21 22 23 24 2 : 31 32 33 34 3 : 41 42 43 44 4 : 51 52 53 54 R8SM_PRINT_SOME_TEST R8SM_PRINT_SOME prints some of an R8SM matrix M = 9 N = 9 Rows 2-5, Cols 3-7: Col: 3 4 5 6 7 Row 2 : 34 35 36 37 38 3 : 44 45 46 47 48 4 : 54 55 56 57 58 5 : 64 65 66 67 68 R8SM_RANDOM_TEST R8SM_RANDOM sets up an R8SM random matrix M = 5 N = 4 The R8SM random matrix: Col: 0 1 2 3 Row 0 : 0.169803 -0.397311 -0.141921 -0.174187 1 : 0.664069 -0.268794 0.146913 -0.080472 2 : -0.0965995 -0.417434 0.41929 -0.360265 3 : -0.014789 -0.0499792 0.382854 0.385447 4 : 0.130787 0.0357189 -0.392222 0.0544345 R8SM_SL_TEST R8SM_SL implements the Sherman-Morrison method for solving a perturbed linear system. Matrix rows M = 5 Matrix columns N = 5 The Sherman-Morrison matrix A: Col: 0 1 2 3 4 Row 0 : 0.673273 0.39638 0.973647 0.978527 0.193452 1 : 0.326952 -0.0226256 0.0316976 0.559813 0.600935 2 : 0.357233 -0.165933 0.0509968 -0.393479 0.465438 3 : -0.266001 -0.13299 0.349846 0.592852 0.637023 4 : 0.283585 -0.16547 0.216226 0.4047 0.542777 The right hand side vector B: 0: 2.7528 1: -1.50598 2: 3.67055 3: 5.31263 4: 8.05361 Solution to A * X = B: 0: 1 1: 2 2: 3 3: 4 4: 5 The Sherman-Morrison matrix A: Col: 0 1 2 3 4 Row 0 : 0.344216 -0.254809 0.273815 0.1468 0.48768 1 : 0.676986 0.470666 0.0847978 -0.0380855 -0.0379347 2 : 0.488362 -0.0515613 0.725721 -0.123095 -0.0344127 3 : -0.183269 0.149558 -0.0689521 -0.595485 0.410509 4 : 0.117944 -0.498884 -0.453547 -0.328947 0.652599 The right hand side vector B: 0: 3.68164 1: 1.5307 2: 1.89796 3: -0.420404 4: -0.293257 Solution to A * X = B: 0: 1 1: 2 2: 3 3: 4 4: 5 R8SM_TO_R8GE_TEST R8SM_TO_R8GE converts an R8SM matrix to R8GE format. M = 5 N = 4 The R8SM matrix: Col: 0 1 2 3 Row 0 : 11 12 13 14 1 : 21 22 23 24 2 : 31 32 33 34 3 : 41 42 43 44 4 : 51 52 53 54 The R8GE matrix: [[11. 12. 13. 14.] [21. 22. 23. 24.] [31. 32. 33. 34.] [41. 42. 43. 44.] [51. 52. 53. 54.]] R8SM_ZEROS_TEST R8SM_ZEROS sets up an R8SM zero matrix M = 5 N = 4 The R8SM zeros matrix: Col: 0 1 2 3 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : 0 0 0 0 3 : 0 0 0 0 4 : 0 0 0 0 r8sm_test(): Normal end of execution. Wed Oct 8 08:50:35 2025