11 April 2023 10:42:24.795 AM 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 0.956318 0.561695 2 0.829509 0.415307 0.257578 3 0.661187E-01 0.109957 0.633966 4 0.438290E-01 0.617272E-01 0.401306 5 0.449539 0.754673 6 0.797287 7 8 9 10 11 12 0.218418 Col: 6 7 8 9 10 Row --- 5 0.183837E-02 6 0.897504 0.945448E-01 7 0.350752 0.136169E-01 0.840847 8 0.859097 0.123104 0.260303 9 0.751236E-02 0.912484 0.351629 10 0.113664 0.822887 11 0.267132 Col: 11 12 Row --- 1 0.597917 2 3 4 5 6 7 8 9 10 0.692066 11 0.561662 0.453794 12 0.861216 0.911977 R83P_DET computes the determinant = -0.419241E-04 R8GE_DET computes the determinant = -0.419241E-04 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 4.75103 4.75103 2 2.43286 2.43286 3 2.99797 2.99797 4 2.38493 2.38493 5 5.58255 5.58255 6 10.0333 10.0333 7 8.92661 8.92661 8 9.34124 9.34124 9 11.7887 11.7887 10 9.47027 9.47027 A'*x and (PLU)'*x 1 9.20476 9.20476 2 4.07150 4.07150 3 4.25034 4.25034 4 4.68854 4.68854 5 5.55404 5.55404 6 6.37390 6.37390 7 11.2175 11.2175 8 12.6837 12.6837 9 17.7342 17.7342 10 14.8961 14.8961 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 0.956318 0.561695 0.797287 2 0.829509 0.415307 0.257578 3 0.661187E-01 0.109957 0.633966 4 0.438290E-01 0.617272E-01 0.401306 5 0.218418 0.449539 0.754673 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 0.956318 0.561695 0.797287 2 0.829509 0.415307 0.257578 3 0.661187E-01 0.109957 0.633966 4 0.438290E-01 0.617272E-01 0.401306 5 0.218418 0.449539 0.754673 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 0.956318 0.561695 0.00000 0.00000 0.797287 2 0.829509 0.415307 0.257578 0.00000 0.00000 3 0.00000 0.661187E-01 0.109957 0.633966 0.00000 4 0.00000 0.00000 0.438290E-01 0.617272E-01 0.401306 5 0.218418 0.00000 0.00000 0.449539 0.754673 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. 11 April 2023 10:42:24.796 AM