10 April 2023 7:50:23.440 PM r8pbu_test(): FORTRAN90 version: Test r8pbu(). R8PBU_CG_TEST R8PBU_CG applies the conjugate gradient method to a symmetric positive definite banded linear system. Matrix order N = 50 Upper bandwidth MU = 1 The symmetric banded matrix: Col: 1 2 3 4 5 Row --- 1 2.00000 -1.00000 2 -1.00000 2.00000 -1.00000 3 -1.00000 2.00000 -1.00000 4 -1.00000 2.00000 -1.00000 5 -1.00000 2.00000 6 -1.00000 Col: 6 7 8 9 10 Row --- 5 -1.00000 6 2.00000 -1.00000 7 -1.00000 2.00000 -1.00000 8 -1.00000 2.00000 -1.00000 9 -1.00000 2.00000 -1.00000 10 -1.00000 2.00000 Solution: 1 1.000000 2 2.000000 3 3.000000 4 4.000000 5 5.000000 6 6.000000 7 7.000000 8 8.000000 ...... .............. 50 50.000000 Maximum residual = 0.568434E-13 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 2.43180 0.561695 0.415307 0.661187E-01 3 0.956318 0.561695 2.15981 0.257578 0.109957 4 0.829509 0.415307 0.257578 3.59212 0.633966 5 0.661187E-01 0.109957 0.633966 5.05543 6 0.438290E-01 0.617272E-01 0.401306 7 0.449539 0.754673 8 0.797287 Col: 6 7 8 9 10 Row --- 3 0.438290E-01 4 0.617272E-01 0.449539 5 0.401306 0.754673 0.797287 6 2.23897 0.183837E-02 0.897504 0.350752 7 0.183837E-02 3.69430 0.945448E-01 0.136169E-01 0.859097 8 0.897504 0.945448E-01 4.31532 0.840847 0.123104 9 0.350752 0.136169E-01 0.840847 2.27576 0.751236E-02 10 0.859097 0.123104 0.751236E-02 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 0.425643E-01 3 0.600217 0.308625 1.30549 -0.944052E-01 0.741640E-01 4 0.520628 0.221411 -0.944052E-01 1.80641 0.349611 5 0.425643E-01 0.741640E-01 0.349611 2.21943 6 0.335728E-01 0.359257E-01 0.174034 7 0.248857 0.300829 8 0.359230 Col: 6 7 8 9 10 Row --- 3 0.335728E-01 4 0.359257E-01 0.248857 5 0.174034 0.300829 0.359230 6 1.48535 -0.400285E-01 0.562148 0.236141 7 -0.400285E-01 1.88156 0.477260E-02 0.122607E-01 0.456587 8 0.562148 0.477260E-02 1.96729 0.359907 0.614676E-01 9 0.236141 0.122607E-01 0.359907 1.44579 -0.139773E-01 10 0.456587 0.614676E-01 -0.139773E-01 1.11397 R8PBU_DET computes the determinant = 13158.4 R8GE_DET computes the determinant = 13158.4 R8PBU_DIF2_TEST R8PBU_DIF2 sets up an R8PBU second difference matrix. Matrix order N = 9 Bandwidth MU = 3 The R8PBU second difference matrix: Col: 1 2 3 4 5 Row --- 1 2.00000 -1.00000 0.00000 0.00000 2 -1.00000 2.00000 -1.00000 0.00000 0.00000 3 0.00000 -1.00000 2.00000 -1.00000 0.00000 4 0.00000 0.00000 -1.00000 2.00000 -1.00000 5 0.00000 0.00000 -1.00000 2.00000 6 0.00000 0.00000 -1.00000 7 0.00000 0.00000 8 0.00000 Col: 6 7 8 9 Row --- 3 0.00000 4 0.00000 0.00000 5 -1.00000 0.00000 0.00000 6 2.00000 -1.00000 0.00000 0.00000 7 -1.00000 2.00000 -1.00000 0.00000 8 0.00000 -1.00000 2.00000 -1.00000 9 0.00000 0.00000 -1.00000 2.00000 R8PBU_FA_TEST R8PBU_FA factors a banded positive definite symmetric matrix, Matrix order N = 50 Upper bandwidth MU = 1 Solution: 1 1.000000 2 2.000000 3 3.000000 4 4.000000 5 5.000000 6 6.000000 7 7.000000 8 8.000000 ...... .............. 50 50.000000 R8PBU_INDICATOR_TEST R8PBU_INDICATOR sets up an R8PBU indicator matrix. Matrix order N = 9 Bandwidth MU = 3 The R8PBU indicator matrix: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 13.0000 14.0000 2 12.0000 22.0000 23.0000 24.0000 25.0000 3 13.0000 23.0000 33.0000 34.0000 35.0000 4 14.0000 24.0000 34.0000 44.0000 45.0000 5 25.0000 35.0000 45.0000 55.0000 6 36.0000 46.0000 56.0000 7 47.0000 57.0000 8 58.0000 Col: 6 7 8 9 Row --- 3 36.0000 4 46.0000 47.0000 5 56.0000 57.0000 58.0000 6 66.0000 67.0000 68.0000 69.0000 7 67.0000 77.0000 78.0000 79.0000 8 68.0000 78.0000 88.0000 89.0000 9 69.0000 79.0000 89.0000 99.0000 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 42.3440 42.3440 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 0.661187E-01 4 0.561695 0.415307 1.32140 0.257578 5 0.661187E-01 0.257578 0.483706 Vector x: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 Product b=A*x 1 4.62079 2 8.33495 3 15.7700 4 8.94282 5 3.64720 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 11.0000 12.0000 13.0000 14.0000 2 12.0000 22.0000 23.0000 24.0000 25.0000 3 13.0000 23.0000 33.0000 34.0000 35.0000 4 14.0000 24.0000 34.0000 44.0000 45.0000 5 25.0000 35.0000 45.0000 55.0000 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 45.0000 46.0000 47.0000 48.0000 5 55.0000 56.0000 57.0000 58.0000 59.0000 6 56.0000 66.0000 67.0000 68.0000 69.0000 7 57.0000 67.0000 77.0000 78.0000 79.0000 8 58.0000 68.0000 78.0000 88.0000 89.0000 R8PBU_RANDOM_TEST R8PBU_RANDOM randomizes an R8PBU matrix. Matrix order N = 10 Upper bandwidth MU = 1 The R8PBU matrix: Col: 1 2 3 4 5 Row --- 1 0.373228 0.218418 2 0.218418 1.25787 0.956318 3 0.956318 2.60312 0.829509 4 0.829509 1.96352 0.561695 5 0.561695 1.73187 6 0.415307 Col: 6 7 8 9 10 Row --- 5 0.415307 6 0.883233 0.661187E-01 7 0.661187E-01 0.334310 0.257578 8 0.257578 0.716373 0.109957 9 0.109957 0.221234 0.438290E-01 10 0.438290E-01 0.589182E-01 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 0.661187E-01 4 0.561695 0.415307 1.32140 0.257578 5 0.661187E-01 0.257578 0.483706 Exact solution x: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 Right hand side b: 1 4.62079 2 8.33495 3 15.7700 4 8.94282 5 3.64720 Approximate solution x2: 1 1.00401 2 2.00755 3 3.00797 4 4.00002 5 5.00898 Residual r = b-A*x2: 1 -0.145501E-01 2 -0.202590E-01 3 -0.403656E-01 4 -0.988622E-02 5 -0.487317E-02 R8PBU_SL_TEST R8PBU_SL solves a linear system that was factored by R8PBU_FA. Matrix order N = 50 Upper bandwidth MU = 1 Solution: 1 1.000000 2 2.000000 3 3.000000 4 4.000000 5 5.000000 6 6.000000 7 7.000000 8 8.000000 ...... .............. 50 50.000000 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 0.001623 2 0.067310 3 0.132722 4 0.197589 5 0.261647 6 0.324632 7 0.386286 8 0.446356 ...... .............. 50 0.001623 Maximum error = 0.999603E-04 SOR iteration. Relaxation factor OMEGA = 0.750000 Iterations taken = 1693 Solution: 1 0.001623 2 0.067309 3 0.132721 4 0.197588 5 0.261645 6 0.324630 7 0.386284 8 0.446354 ...... .............. 50 0.001623 Maximum error = 0.999408E-04 SOR iteration. Relaxation factor OMEGA = 1.00000 Iterations taken = 1269 Solution: 1 0.001624 2 0.067312 3 0.132725 4 0.197593 5 0.261652 6 0.324638 7 0.386293 8 0.446365 ...... .............. 50 0.001624 Maximum error = 0.999855E-04 R8PBU_TO_R8GE_TEST R8PBU_TO_R8GE converts an R8PBU matrix to R8GE format. Matrix order N = 5 Bandwidth MU = 3 The R8PBU matrix: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 13.0000 14.0000 2 12.0000 22.0000 23.0000 24.0000 25.0000 3 13.0000 23.0000 33.0000 34.0000 35.0000 4 14.0000 24.0000 34.0000 44.0000 45.0000 5 25.0000 35.0000 45.0000 55.0000 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 13.0000 14.0000 0.00000 2 12.0000 22.0000 23.0000 24.0000 25.0000 3 13.0000 23.0000 33.0000 34.0000 35.0000 4 14.0000 24.0000 34.0000 44.0000 45.0000 5 0.00000 25.0000 35.0000 45.0000 55.0000 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 0.00000 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 0.00000 0.00000 5 0.00000 0.00000 0.00000 0.00000 6 0.00000 0.00000 0.00000 7 0.00000 0.00000 8 0.00000 Col: 6 7 8 9 Row --- 3 0.00000 4 0.00000 0.00000 5 0.00000 0.00000 0.00000 6 0.00000 0.00000 0.00000 0.00000 7 0.00000 0.00000 0.00000 0.00000 8 0.00000 0.00000 0.00000 0.00000 9 0.00000 0.00000 0.00000 0.00000 r8pbu_test(): Normal end of execution. 10 April 2023 7:50:23.450 PM