08-Oct-2025 14:14:55 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: 9.6411 9.6411 2: 4.30548 4.30548 3: 6.1924 6.1924 4: 4.60811 4.60811 5: 7.74766 7.74766 6: 9.17823 9.17823 7: 14.9269 14.9269 8: 11.6057 11.6057 9: 9.01078 9.01078 10: 7.86248 7.86248 A'*x and (PLU)'*x 1: 4.16365 4.16365 2: 4.10405 4.10405 3: 5.95951 5.95951 4: 4.2934 4.2934 5: 5.00234 5.00234 6: 7.16093 7.16093 7: 3.24376 3.24376 8: 15.9294 15.9294 9: 18.5562 18.5562 10: 12.0805 12.0805 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: 0.78944 0.829829 0.174831 2: 0.377569 0.519569 0.266932 3: 0.609741 0.951374 0.0324251 4: 0.558027 0.966239 0.227706 5: 0.607349 0.586863 0.983682 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: 0.156977 0.169869 0.797535 2: 0.505741 0.934249 0.785097 3: 0.595766 0.717497 0.716713 4: 0.887408 0.564218 0.483187 5: 0.00136454 0.871042 0.437934 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 0.156977 0.169869 0 0 0.797535 2 0.505741 0.934249 0.785097 0 0 3 0 0.595766 0.717497 0.716713 0 4 0 0 0.887408 0.564218 0.483187 5 0.00136454 0 0 0.871042 0.437934 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. 08-Oct-2025 14:14:55