17-May-2023 09:06:17 r83p_test(): MATLAB version Test r83p(). R83P_DET_TEST R83P_DET, determinant of a tridiagonal periodic matrix. Matrix order N = 12 The periodic tridiagonal matrix: Col: 1 2 3 4 5 Row --- 1: 11 12 15 2: 21 22 23 3: 32 33 34 4: 43 44 45 5: 51 54 55 R83P_DET computes the determinant = 7.077246e+07 R8GE_DET computes the determinant = 7.077246e+07 R83P_FA_TEST R83P_FA factors a tridiagonal periodic system which then can be solved by R83P_SL. Matrix order N = 10 Solution: 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 9: 9 10: 10 Solution to transposed system: 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 9: 9 10: 10 R83P_INDICATOR_TEST R83P_INDICATOR sets up an R83P indicator matrix. Matrix order N = 10 The R83P indicator matrix: Col: 1 2 3 4 5 Row --- 1: 101 102 2: 201 202 203 3: 302 303 304 4: 403 404 405 5: 504 505 6: 605 7: 8: 9: 10: 1001 Col: 6 7 8 9 10 Row --- 1: 110 2: 3: 4: 5: 506 6: 606 607 7: 706 707 708 8: 807 808 809 9: 908 909 910 10: 1009 1010 R83P_ML_TEST R83P_ML computes A*x or A'*X where A has been factored by R83P_FA. Matrix order N = 10 A*x and PLU*x 1: 9.11436 9.11436 2: 1.82938 1.82938 3: 5.24293 5.24293 4: 6.11971 6.11971 5: 3.87702 3.87702 6: 6.65127 6.65127 7: 12.4103 12.4103 8: 22.4105 22.4105 9: 20.044 20.044 10: 12.4511 12.4511 A'*x and (PLU)'*x 1: 7.79166 7.79166 2: 1.49948 1.49948 3: 5.9505 5.9505 4: 7.82884 7.82884 5: 12.7692 12.7692 6: 9.93349 9.93349 7: 13.5211 13.5211 8: 19.842 19.842 9: 13.8632 13.8632 10: 16.0585 16.0585 R83P_MTV_TEST R83P_MTV computes A'*x=b for an R83P matrix. Matrix order N = 5 The R83P matrix A: Col: 1 2 3 4 5 Row --- 1: 11 12 15 2: 21 22 23 3: 32 33 34 4: 43 44 45 5: 51 54 55 The vector X: 1: 1 2: 2 3: 3 4: 4 5: 5 The product b = A'*x: 1: 308 2: 152 3: 317 4: 548 5: 470 R83P_MV_TEST R83P_MV computes A*x=b for an R83P matrix. Matrix order N = 5 The R83P matrix A: Col: 1 2 3 4 5 Row --- 1: 11 12 15 2: 21 22 23 3: 32 33 34 4: 43 44 45 5: 51 54 55 The vector X: 1: 1 2: 2 3: 3 4: 4 5: 5 The product b = A*x: 1: 110 2: 134 3: 299 4: 530 5: 542 R83P_PRINT_TEST R83P_PRINT prints an R83P matrix. Matrix order N = 5 The R83P matrix: Col: 1 2 3 4 5 Row --- 1: 11 12 15 2: 21 22 23 3: 32 33 34 4: 43 44 45 5: 51 54 55 R83P_PRINT_SOME_TEST R83P_PRINT_SOME prints some of an R83P matrix. Matrix order N = 10 Rows 1:N, Cols 1:2: Col: 1 2 Row --- 1: 101 102 2: 201 202 3: 302 4: 5: 6: 7: 8: 9: 10: 1001 R83P_RANDOM_TEST R83P_RANDOM sets up a random R83P matrix. Matrix order N = 5 The R83P matrix: Col: 1 2 3 4 5 Row --- 1: 0.567661 0.678219 0.0621331 2: 0.868031 0.622285 0.271189 3: 0.710268 0.373861 0.490674 4: 0.56231 0.126207 0.81927 5: 0.0823429 0.124238 0.791729 R83P_SL_TEST R83P_SL solves a tridiagonal periodic system after it has been factored by R83P_FA. Matrix order N = 10 Solution: 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 9: 9 10: 10 Solution to transposed system: 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 9: 9 10: 10 R83P_TO_R8GE_TEST R83P_TO_R8GE converts a matrix from R83P to R8GE format. Matrix order N = 5 The R83P matrix: Col: 1 2 3 4 5 Row --- 1: 0.859282 0.81709 0.600158 2: 0.899079 0.771207 0.467912 3: 0.169918 0.497461 0.604422 4: 0.0554424 0.223744 0.458227 5: 0.947554 0.106962 0.243116 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 0.859282 0.81709 0 0 0.600158 2 0.899079 0.771207 0.467912 0 0 3 0 0.169918 0.497461 0.604422 0 4 0 0 0.0554424 0.223744 0.458227 5 0.947554 0 0 0.106962 0.243116 R83P_ZEROS_TEST R83P_ZEROS sets up a zero R83P matrix. Matrix order N = 5 The R83P matrix: Col: 1 2 3 4 5 Row --- 1: 0 0 0 2: 0 0 0 3: 0 0 0 4: 0 0 0 5: 0 0 0 r83p_test() Normal end of execution. 17-May-2023 09:06:17