20-May-2023 21:05:27 r8pbu_test(): MATLAB version Test r8pbu(). R8PBU_CG_TEST R8PBU_CG applies CG to an R8PBU matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 1.63216e-15 Norm of error ||x1-x2|| = 6.54908e-16 R8PBU_DET_TEST R8PBU_DET, determinant of a positive definite symmetric banded matrix. Matrix order N = 10 Upper bandwidth MU = 3 The R8PBU matrix: Col: 1 2 3 4 5 Row --- 1 2.53856 0.218418 0.956318 0.829509 2 0.218418 2.4318 0.561695 0.415307 0.0661187 3 0.956318 0.561695 2.15981 0.257578 0.109957 4 0.829509 0.415307 0.257578 3.59212 0.633966 5 0.0661187 0.109957 0.633966 5.05543 6 0.043829 0.0617272 0.401306 7 0.449539 0.754673 8 0.797287 Col: 6 7 8 9 10 Row --- 3 0.043829 4 0.0617272 0.449539 5 0.401306 0.754673 0.797287 6 2.23897 0.00183837 0.897504 0.350752 7 0.00183837 3.6943 0.0945448 0.0136169 0.859097 8 0.897504 0.0945448 4.31532 0.840847 0.123104 9 0.350752 0.0136169 0.840847 2.27576 0.00751236 10 0.859097 0.123104 0.00751236 1.45338 The R8PBU factored matrix: Col: 1 2 3 4 5 Row --- 1 1.59329 0.137087 0.600217 0.520628 2 0.137087 1.55339 0.308625 0.221411 0.0425643 3 0.600217 0.308625 1.30549 -0.0944052 0.074164 4 0.520628 0.221411 -0.0944052 1.80641 0.349611 5 0.0425643 0.074164 0.349611 2.21943 6 0.0335728 0.0359257 0.174034 7 0.248857 0.300829 8 0.35923 Col: 6 7 8 9 10 Row --- 3 0.0335728 4 0.0359257 0.248857 5 0.174034 0.300829 0.35923 6 1.48535 -0.0400285 0.562148 0.236141 7 -0.0400285 1.88156 0.0047726 0.0122607 0.456587 8 0.562148 0.0047726 1.96729 0.359907 0.0614676 9 0.236141 0.0122607 0.359907 1.44579 -0.0139773 10 0.456587 0.0614676 -0.0139773 1.11397 R8PBU_DET computes the determinant = 13158.441270 R8GE_DET computes the determinant = 13158.441270 R8PBU_DIF2_TEST R8PBU_DIF2 sets up a R8PBU second difference matrix. Matrix order M = 5 Matrix order N = 5 Bandwidth MU = 1 The R8PBU second difference matrix: Col: 1 2 3 4 5 Row --- 1 2 -1 2 -1 2 -1 3 -1 2 -1 4 -1 2 -1 5 -1 2 R8PBU_FA_TEST R8PBU_FA factors an R8PBU matrix. Matrix order N = 50 Upper bandwidth MU = 1 Solution: 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 ...... .............. 50 50 R8PBU_INDICATOR_TEST R8PBU_INDICATOR sets up a R8PBU indicator matrix. Matrix order N = 9 Bandwidth MU = 3 The R8PBU indicator matrix: Col: 1 2 3 4 5 Row --- 1 11 12 13 14 2 12 22 23 24 25 3 13 23 33 34 35 4 14 24 34 44 45 5 25 35 45 55 6 36 46 56 7 47 57 8 58 Col: 6 7 8 9 Row --- 3 36 4 46 47 5 56 57 58 6 66 67 68 69 7 67 77 78 79 8 68 78 88 89 9 69 79 89 99 R8PBU_ML_TEST R8PBU_ML computes A*x where A has been factored by R8PBU_FA. Matrix order N = 10 Upper bandwidth MU = 3 A*x and PLU*x 1: 9.16239 9.16239 2: 8.75892 8.75892 3: 10.4022 10.4022 4: 23.4883 23.4883 5: 42.344 42.344 6: 26.1684 26.1684 7: 40.9126 40.9126 8: 53.3545 53.3545 9: 29.4836 29.4836 10: 21.5999 21.5999 R8PBU_MV_TEST R8PBU_MV computes A*x Matrix order N = 5 Upper bandwidth MU = 2 Matrix A: Col: 1 2 3 4 5 Row --- 1 1.31501 0.218418 0.956318 2 0.218418 1.69061 0.829509 0.561695 3 0.956318 0.829509 3.72095 0.415307 0.0661187 4 0.561695 0.415307 1.3214 0.257578 5 0.0661187 0.257578 0.483706 Vector x: 1: 1 2: 2 3: 3 4: 4 5: 5 Product b=A*x 1: 4.62079 2: 8.33495 3: 15.77 4: 8.94282 5: 3.6472 R8PBU_PRINT_TEST R8PBU_PRINT prints an R8PBU matrix. Matrix order N = 5 Bandwidth MU = 3 The R8PBU matrix: Col: 1 2 3 4 5 Row --- 1 11 12 13 14 2 12 22 23 24 25 3 13 23 33 34 35 4 14 24 34 44 45 5 25 35 45 55 R8PBU_PRINT_SOME_TEST R8PBU_PRINT_SOME prints some of an R8PBU matrix. Matrix order N = 9 Bandwidth MU = 4 Row(4:8), Col(5:9): Col: 5 6 7 8 9 Row --- 4 45 46 47 48 5 55 56 57 58 59 6 56 66 67 68 69 7 57 67 77 78 79 8 58 68 78 88 89 R8PBU_RANDOM_TEST R8PBU_RANDOM sets up a random R8PBU matrix. Matrix order N = 9 Bandwidth MU = 3 Seed = 123456789 The R8PBU matrix: Col: 1 2 3 4 5 Row --- 1 3.70792 0.218418 0.956318 0.829509 2 0.218418 1.42807 0.561695 0.415307 0.0661187 3 0.956318 0.561695 1.95395 0.257578 0.109957 4 0.829509 0.415307 0.257578 3.34941 0.633966 5 0.0661187 0.109957 0.633966 5.30391 6 0.043829 0.0617272 0.401306 7 0.449539 0.754673 8 0.797287 Col: 6 7 8 9 Row --- 3 0.043829 4 0.0617272 0.449539 5 0.401306 0.754673 0.797287 6 1.9678 0.00183837 0.897504 0.350752 7 0.00183837 1.78984 0.0945448 0.0136169 8 0.897504 0.0945448 4.84602 0.859097 9 0.350752 0.0136169 0.859097 1.56296 R8PBU_RES_TEST R8PBU_RES returns the residual b-A*x where A is a positive definite symmetric band matrix. Matrix order N = 5 Upper bandwidth MU = 2 Matrix A: Col: 1 2 3 4 5 Row --- 1 1.31501 0.218418 0.956318 2 0.218418 1.69061 0.829509 0.561695 3 0.956318 0.829509 3.72095 0.415307 0.0661187 4 0.561695 0.415307 1.3214 0.257578 5 0.0661187 0.257578 0.483706 Exact solution x: 1: 1 2: 2 3: 3 4: 4 5: 5 Right hand side b: 1: 4.62079 2: 8.33495 3: 15.77 4: 8.94282 5: 3.6472 Approximate solution x2: 1: 1.00401 2: 2.00755 3: 3.00797 4: 4.00002 5: 5.00898 Residual r = b-A*x2: 1: -0.0145501 2: -0.020259 3: -0.0403656 4: -0.00988622 5: -0.00487317 R8PBU_SL_TEST R8PBU_SL solves a linear system factored by R8PBU_FA. Matrix order N = 50 Upper bandwidth MU = 1 Solution: 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 ...... .............. 50 50 R8PBU_SOR_TEST R8PBU_SOR, SOR routine for iterative solution of A*x=b. Matrix order N = 50 Upper bandwidth MU = 1 SOR iteration. Relaxation factor OMEGA = 0.250000 Iterations taken = 5081 Solution: 1 0.00162299 2 0.06731 3 0.132722 4 0.197589 5 0.261647 6 0.324632 7 0.386286 8 0.446356 ...... .............. 50 0.00162299 Maximum error = 0.000100 SOR iteration. Relaxation factor OMEGA = 0.750000 Iterations taken = 1693 Solution: 1 0.00162268 2 0.0673094 3 0.132721 4 0.197588 5 0.261645 6 0.32463 7 0.386284 8 0.446354 ...... .............. 50 0.00162268 Maximum error = 0.000100 SOR iteration. Relaxation factor OMEGA = 1.000000 Iterations taken = 1269 Solution: 1 0.00162404 2 0.0673122 3 0.132725 4 0.197593 5 0.261652 6 0.324638 7 0.386293 8 0.446365 ...... .............. 50 0.00162404 Maximum error = 0.000100 R8PBU_TO_R8GE_TEST R8PBU_TO_R9GE converts an R8PBU matrix to R8GE format. Matrix order N = 9 Bandwidth MU = 3 The R8PBU matrix: Col: 1 2 3 4 5 Row --- 1 11 12 13 14 2 12 22 23 24 25 3 13 23 33 34 35 4 14 24 34 44 45 5 25 35 45 55 6 36 46 56 7 47 57 8 58 Col: 6 7 8 9 Row --- 3 36 4 46 47 5 56 57 58 6 66 67 68 69 7 67 77 78 79 8 68 78 88 89 9 69 79 89 99 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 11 12 13 14 0 2 12 22 23 24 25 3 13 23 33 34 35 4 14 24 34 44 45 5 0 25 35 45 55 6 0 0 36 46 56 7 0 0 0 47 57 8 0 0 0 0 58 9 0 0 0 0 0 Col: 6 7 8 9 Row --- 1 0 0 0 0 2 0 0 0 0 3 36 0 0 0 4 46 47 0 0 5 56 57 58 0 6 66 67 68 69 7 67 77 78 79 8 68 78 88 89 9 69 79 89 99 R8PBU_ZEROS_TEST R8PBU_ZEROS sets up an R8PBU zero matrix. Matrix order N = 9 Bandwidth MU = 3 The R8PBU zero matrix: Col: 1 2 3 4 5 Row --- 1 0 0 0 0 2 0 0 0 0 0 3 0 0 0 0 0 4 0 0 0 0 0 5 0 0 0 0 6 0 0 0 7 0 0 8 0 Col: 6 7 8 9 Row --- 3 0 4 0 0 5 0 0 0 6 0 0 0 0 7 0 0 0 0 8 0 0 0 0 9 0 0 0 0 r8pbu_test(): Normal end of execution. 20-May-2023 21:06:08