16-Aug-2022 17:47:32 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: 0.905792 0.913376 2: 0.126987 0.632359 0.278498 3: 0.0975404 0.546882 0.964889 4: 0.957507 0.157613 0.957167 5: 0.970593 0.485376 6: 0.80028 7: 8: 9: 10: 11: 12: 0.814724 Col: 6 7 8 9 10 Row --- 5: 0.141886 6: 0.421761 0.792207 7: 0.915736 0.959492 0.0357117 8: 0.655741 0.849129 0.678735 9: 0.933993 0.75774 0.392227 10: 0.743132 0.655478 11: 0.171187 Col: 11 12 Row --- 1: 0.823458 2: 3: 4: 5: 6: 7: 8: 9: 10: 0.706046 11: 0.0318328 0.0461714 12: 0.276923 0.0971318 R83P_DET computes the determinant = 1.820547e-03 R8GE_DET computes the determinant = 1.820547e-03 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: 1.9527 1.9527 2: 4.27358 4.27358 3: 2.63907 2.63907 4: 6.6544 6.6544 5: 8.35575 8.35575 6: 11.6902 11.6902 7: 11.329 11.329 8: 9.02666 9.02666 9: 12.8198 12.8198 10: 14.6645 14.6645 A'*x and (PLU)'*x 1: 6.18143 6.18143 2: 3.04434 3.04434 3: 2.87062 2.87062 4: 6.12823 6.12823 5: 9.20087 9.20087 6: 8.18633 8.18633 7: 11.0017 11.0017 8: 11.5825 11.5825 9: 9.55665 9.55665 10: 16.0159 16.0159 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: 0.399783 0.800068 0.853031 2: 0.25987 0.431414 0.181847 3: 0.910648 0.263803 0.136069 4: 0.145539 0.869292 0.54986 5: 0.0844358 0.579705 0.144955 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: 0.821194 0.0430238 0.183511 2: 0.0154034 0.16899 0.731722 3: 0.649115 0.647746 0.547009 4: 0.450924 0.296321 0.188955 5: 0.353159 0.744693 0.686775 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 0.821194 0.0430238 0 0 0.183511 2 0.0154034 0.16899 0.731722 0 0 3 0 0.649115 0.647746 0.547009 0 4 0 0 0.450924 0.296321 0.188955 5 0.353159 0 0 0.744693 0.686775 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. 16-Aug-2022 17:47:32