09 May 2025 9:29:07.849 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 0.302793 0.973985 2 0.841699 0.995499 0.906969 3 0.765628E-02 0.839777E-01 0.319559E-01 4 0.845326 0.711876 0.712105 5 0.616035E-01 0.146740 6 0.746647 7 8 9 10 11 12 0.210948E-01 Col: 6 7 8 9 10 Row --- 5 0.197380 6 0.177140 0.932647 7 0.273160 0.513525 0.461896 8 0.748473 0.380458 0.179075 9 0.854935 0.853228E-01 0.428094 10 0.457969 0.466144 11 0.708086E-01 Col: 11 12 Row --- 1 0.637268 2 3 4 5 6 7 8 9 10 0.997608 11 0.948646E-01 0.351033 12 0.473189 0.398666 R83P_DET computes the determinant = 0.135979E-04 R8GE_DET computes the determinant = 0.135979E-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 10.4848 10.4848 2 3.27170 3.27170 3 3.32856 3.32856 4 4.47155 4.47155 5 8.15479 8.15479 6 7.62743 7.62743 7 11.8865 11.8865 8 4.46570 4.46570 9 15.3266 15.3266 10 9.28722 9.28722 A'*x and (PLU)'*x 1 2.17599 2.17599 2 1.33324 1.33324 3 4.77810 4.77810 4 7.89168 7.89168 5 2.58132 2.58132 6 7.66837 7.66837 7 15.3966 15.3966 8 11.7674 11.7674 9 18.3139 18.3139 10 4.79248 4.79248 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 0.718491 0.960321 0.630582 2 0.452546 0.511227E-01 0.251266 3 0.920339 0.871058 0.838158 4 0.350369 0.355930 0.586308 5 0.904560 0.105582 0.770455 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 0.156146E-02 0.885066 0.612739 2 0.488010 0.548339 0.766760 3 0.286778E-01 0.300041 0.725988 4 0.989754 0.428723E-02 0.291943 5 0.733576 0.660422 0.798314 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 0.156146E-02 0.885066 0.00000 0.00000 0.612739 2 0.488010 0.548339 0.766760 0.00000 0.00000 3 0.00000 0.286778E-01 0.300041 0.725988 0.00000 4 0.00000 0.00000 0.989754 0.428723E-02 0.291943 5 0.733576 0.00000 0.00000 0.660422 0.798314 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. 09 May 2025 9:29:07.849 PM