Tue May 20 22:27:39 2025 r8sto_test(): python version: 3.10.12 numpy version: 1.26.4 Test r8sto(). Matrix order N = 5 The matrix: Col: 0 1 2 3 4 Row 0 : 2 -1 0 0 0 1 : -1 2 -1 0 0 2 : 0 -1 2 -1 0 3 : 0 0 -1 2 -1 4 : 0 0 0 -1 2 R8STO_INDICATOR_TEST R8STO_INDICATOR sets up a R8STO indicator matrix. Matrix order N = 5 The R8STO indicator matrix: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 12 11 12 13 14 2 : 13 12 11 12 13 3 : 14 13 12 11 12 4 : 15 14 13 12 11 R8STO_INVERSE_TEST R8STO_INVERSE computes the inverse of a positive definite symmetric Toeplitz matrix. Matrix order N = 3 The symmetric Toeplitz matrix A: Col: 0 1 2 Row 0 : 4 2 0.8 1 : 2 4 2 2 : 0.8 2 4 The inverse matrix B: [[ 0.33482143 -0.17857143 0.02232143] [-0.17857143 0.42857143 -0.17857143] [ 0.02232143 -0.17857143 0.33482143]] The product C = A * B: [[ 1.00000000e+00 3.64787565e-17 -7.33540213e-18] [ 4.16333634e-17 1.00000000e+00 0.00000000e+00] [ 2.77555756e-17 0.00000000e+00 1.00000000e+00]] R8STO_MV_TEST R8STO_MV computes b=A*x, where A is an R8STO matrix. Matrix order N = 5 The R8STO matrix: Col: 0 1 2 3 4 Row 0 : 0.27778 0.668613 0.812133 0.52529 0.479939 1 : 0.668613 0.27778 0.668613 0.812133 0.52529 2 : 0.812133 0.668613 0.27778 0.668613 0.812133 3 : 0.52529 0.812133 0.668613 0.27778 0.668613 4 : 0.479939 0.52529 0.812133 0.668613 0.27778 x: 0: 1 1: 2 2: 3 3: 4 4: 5 b=A*x: 0: 8.55226 1: 9.10499 2: 9.71781 3: 8.60958 4: 8.03027 R8STO_PRINT_TEST R8STO_PRINT prints an R8STO matrix. Matrix order N = 5 The R8STO matrix: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 12 11 12 13 14 2 : 13 12 11 12 13 3 : 14 13 12 11 12 4 : 15 14 13 12 11 R8STO_PRINT_SOME_TEST R8STO_PRINT_SOME prints some of an R8STO matrix. Matrix order N = 5 Rows 1:4, Cols 0:2 Col: 0 1 2 Row 1 : 12 11 12 2 : 13 12 11 3 : 14 13 12 4 : 15 14 13 R8STO_RANDOM_TEST R8STO_RANDOM randomizes an R8STO matrix. Matrix order N = 5 The R8STO matrix: Col: 0 1 2 3 4 Row 0 : 0.108105 0.670139 0.138222 0.806604 0.196588 1 : 0.670139 0.108105 0.670139 0.138222 0.806604 2 : 0.138222 0.670139 0.108105 0.670139 0.138222 3 : 0.806604 0.138222 0.670139 0.108105 0.670139 4 : 0.196588 0.806604 0.138222 0.670139 0.108105 R8STO_SL_TEST R8STO_SL solves a positive definite symmetric Toeplitz system. Matrix order N = 3 The symmetric Toeplitz matrix A: Col: 0 1 2 Row 0 : 1 0.5 0.2 1 : 0.5 1 0.5 2 : 0.2 0.5 1 The right hand side vector B: 0: 4 1: -1 2: 3 The solution X: 0: 6.33929 1: -6.71429 2: 5.08929 Norm of residual error A * x - b = 0.0 R8STO_TO_R8GE_TEST R8STO_TO_R8GE converts a matrix from R8STO to R8GE format. Matrix order N = 5 The R8STO matrix: Col: 0 1 2 3 4 Row 0 : 0.382442 0.78106 0.310369 0.0493816 0.986325 1 : 0.78106 0.382442 0.78106 0.310369 0.0493816 2 : 0.310369 0.78106 0.382442 0.78106 0.310369 3 : 0.0493816 0.310369 0.78106 0.382442 0.78106 4 : 0.986325 0.0493816 0.310369 0.78106 0.382442 The R8GE matrix: [[0.38244203 0.78106013 0.31036937 0.04938155 0.98632462] [0.78106013 0.38244203 0.78106013 0.31036937 0.04938155] [0.31036937 0.78106013 0.38244203 0.78106013 0.31036937] [0.04938155 0.31036937 0.78106013 0.38244203 0.78106013] [0.98632462 0.04938155 0.31036937 0.78106013 0.38244203]] R8STO_YW_SL_TEST R8STO_YW_SL solves the Yule-Walker equations for a symmetric Toeplitz system. Matrix order N = 3 The symmetric Toeplitz matrix: Col: 0 1 2 Row 0 : 1 0.5 0.2 1 : 0.5 1 0.5 2 : 0.2 0.5 1 The right hand side, B: 0: -0.5 1: -0.2 2: -0.1 The computed solution, X: 0: -0.535714 1: 0.0857143 2: -0.0357143 The product A*x: 0: -0.5 1: -0.2 2: -0.1 R8STO_ZEROS_TEST R8STO_ZEROS zeros an R8STO matrix. Matrix order N = 5 The R8STO matrix: Col: 0 1 2 3 4 Row 0 : 0 0 0 0 0 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 r8sto_test(): Normal end of execution. Tue May 20 22:27:39 2025