06 October 2025 6:33:29.183 PM r83p_test(): Fortran90 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 0.724613 0.618955 2 0.164952 0.352575 0.417894 3 0.599315 0.746200 0.331588 4 0.243881 0.729140E-01 0.617952 5 0.962748 0.228067 6 0.746420 7 8 9 10 11 12 0.904639E-01 Col: 6 7 8 9 10 Row --- 5 0.693892 6 0.674804 0.215011 7 0.259715 0.239397 0.887196E-01 8 0.577693 0.708251E-01 0.739909 9 0.358087 0.459671 0.452043 10 0.637815 0.559329 11 0.955689 Col: 11 12 Row --- 1 0.113849E-01 2 3 4 5 6 7 8 9 10 0.914044 11 0.742269 0.784950 12 0.512364 0.743736E-01 R83P_DET computes the determinant = 0.413370E-03 R8GE_DET computes the determinant = 0.413370E-03 R83P_FA_TEST R83P_FA factors a tridiagonal periodic system which can then be solved by R83P_SL. Matrix order N = 10 Solution: 1: 1.0000000 2: 2.0000000 3: 3.0000000 4: 4.0000000 5: 5.0000000 6: 6.0000000 7: 7.0000000 8: 8.0000000 9: 9.0000000 10: 10.000000 Solution to transposed system: 1: 1.0000000 2: 2.0000000 3: 3.0000000 4: 4.0000000 5: 5.0000000 6: 6.0000000 7: 7.0000000 8: 8.0000000 9: 9.0000000 10: 10.000000 R83P_INDICATOR_TEST R83P_INDICATOR sets up an R83P indicator matrix. Matrix order N = 5 The R83P indicator matrix: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 15.0000 2 21.0000 22.0000 23.0000 3 32.0000 33.0000 34.0000 4 43.0000 44.0000 45.0000 5 51.0000 54.0000 55.0000 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 9.49666 9.49666 2 2.78874 2.78874 3 4.37010 4.37010 4 5.40572 5.40572 5 4.11340 4.11340 6 12.1297 12.1297 7 16.6583 16.6583 8 21.0950 21.0950 9 11.9862 11.9862 10 15.6773 15.6773 A'*x and (PLU)'*x 1 9.85117 9.85117 2 0.817791 0.817791 3 7.30377 7.30377 4 6.49379 6.49379 5 4.30264 4.30264 6 5.72859 5.72859 7 13.5394 13.5394 8 11.5980 11.5980 9 16.0350 16.0350 10 13.0806 13.0806 R83P_MTV_TEST R83P_MTV computes A'*x = b for an R83P matrix. Matrix order N = 5 The R83P indicator matrix: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 15.0000 2 21.0000 22.0000 23.0000 3 32.0000 33.0000 34.0000 4 43.0000 44.0000 45.0000 5 51.0000 54.0000 55.0000 Vector x: 1: 1.0000000 2: 2.0000000 3: 3.0000000 4: 4.0000000 5: 5.0000000 b=A'*x: 1: 308.00000 2: 152.00000 3: 317.00000 4: 548.00000 5: 470.00000 R83P_MV_TEST R83P_MV computes A*x = b for an R83P matrix. Matrix order N = 5 The R83P indicator matrix: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 15.0000 2 21.0000 22.0000 23.0000 3 32.0000 33.0000 34.0000 4 43.0000 44.0000 45.0000 5 51.0000 54.0000 55.0000 Vector x: 1: 1.0000000 2: 2.0000000 3: 3.0000000 4: 4.0000000 5: 5.0000000 b=A*x: 1: 110.00000 2: 134.00000 3: 299.00000 4: 530.00000 5: 542.00000 R83P_PRINT_TEST R83P_PRINT prints an R83P matrix. Matrix order N = 5 An R83P matrix: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 15.0000 2 21.0000 22.0000 23.0000 3 32.0000 33.0000 34.0000 4 43.0000 44.0000 45.0000 5 51.0000 54.0000 55.0000 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 --- 1 101.000 102.000 2 201.000 202.000 3 302.000 4 5 6 7 8 9 10 1001.00 R83P_RANDOM_TEST R83P_RANDOM returns a random R83P matrix. Matrix order N = 5 A random R83P matrix: Col: 1 2 3 4 5 Row --- 1 0.434377 0.209364 0.444014 2 0.479161 0.831873 0.264380 3 0.534040E-01 0.498284 0.168462 4 0.697925 0.976046 0.565371 5 0.667806 0.174661 0.842688 R83P_SL_TEST R83P_SL solves a tridiagonal periodic system after it has been factored bu R83P_FA. Matrix order N = 10 Solution: 1: 1.0000000 2: 2.0000000 3: 3.0000000 4: 4.0000000 5: 5.0000000 6: 6.0000000 7: 7.0000000 8: 8.0000000 9: 9.0000000 10: 10.000000 Solution to transposed system: 1: 1.0000000 2: 2.0000000 3: 3.0000000 4: 4.0000000 5: 5.0000000 6: 6.0000000 7: 7.0000000 8: 8.0000000 9: 9.0000000 10: 10.000000 R83P_TO_R8GE_TEST R83P_TO_R8GE converts an R83P matrix to R8GE format. Matrix order N = 5 The R83P matrix: Col: 1 2 3 4 5 Row --- 1 0.325979 0.486539 0.437407 2 0.539717E-01 0.650705E-02 0.485611E-01 3 0.254745 0.788789 0.835088 4 0.556307E-01 0.809704 0.525727 5 0.407291 0.828717 0.595296 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 0.325979 0.486539 0.00000 0.00000 0.437407 2 0.539717E-01 0.650705E-02 0.485611E-01 0.00000 0.00000 3 0.00000 0.254745 0.788789 0.835088 0.00000 4 0.00000 0.00000 0.556307E-01 0.809704 0.525727 5 0.407291 0.00000 0.00000 0.828717 0.595296 R83P_ZEROS_TEST R83P_ZEROS returns a zero R83P matrix. Matrix order N = 5 A zero R83P matrix: Col: 1 2 3 4 5 Row --- 1 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 5 0.00000 0.00000 0.00000 r83p_test(): Normal end of execution. 06 October 2025 6:33:29.183 PM