28-Aug-2022 10:16:40 r8sto_test(): MATLAB version Test r8sto(). R8STO_DIF2_TEST R8STO_DIF2 sets the second difference as an R8STO matrix. Matrix order N = 5 The R8STO DIF2 matrix: Col: 1 2 3 4 5 Row --- 1 2 -1 0 0 0 2 -1 2 -1 0 0 3 0 -1 2 -1 0 4 0 0 -1 2 -1 5 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: 1 2 3 4 5 Row --- 1 11 12 13 14 15 2 12 11 12 13 14 3 13 12 11 12 13 4 14 13 12 11 12 5 15 14 13 12 11 R8STO_INVERSE_TEST R8STO_INVERSE computes the inverse of a positive definite symmetric Toeplitz matrix. Matrix order N = 5 The symmetric Toeplitz matrix A: Col: 1 2 3 4 5 Row --- 1 4 2 0.8 0.4 0.1 2 2 4 2 0.8 0.4 3 0.8 2 4 2 0.8 4 0.4 0.8 2 4 2 5 0.1 0.4 0.8 2 4 The inverse matrix B: Col: 1 2 3 4 5 Row --- 1 0.335767 -0.180346 0.0299103 -0.0190557 0.0131862 2 -0.180346 0.432116 -0.195663 0.0389708 -0.0190557 3 0.0299103 -0.195663 0.433699 -0.195663 0.0299103 4 -0.0190557 0.0389708 -0.195663 0.432116 -0.180346 5 0.0131862 -0.0190557 0.0299103 -0.180346 0.335767 Maximum discrepancy in A * B - I is 3.426079e-16 R8STO_MV_TEST R8STO_MV computes b=A*x, where A is an R8STO matrix. Matrix order N = 5 The R8STO matrix: Col: 1 2 3 4 5 Row --- 1 0.218418 0.956318 0.829509 0.561695 0.415307 2 0.956318 0.218418 0.956318 0.829509 0.561695 3 0.829509 0.956318 0.218418 0.956318 0.829509 4 0.561695 0.829509 0.956318 0.218418 0.956318 5 0.415307 0.561695 0.829509 0.956318 0.218418 x: 1: 1 2: 2 3: 3 4: 4 5: 5 b=A*x: 1: 8.9429 2: 10.3886 3: 11.3702 4: 10.7449 5: 8.94459 R8STO_PRINT_TEST R8STO_PRINT prints an R8STO matrix. Matrix order N = 5 The R8STO matrix: Col: 1 2 3 4 5 Row --- 1 11 12 13 14 15 2 12 11 12 13 14 3 13 12 11 12 13 4 14 13 12 11 12 5 15 14 13 12 11 R8STO_PRINT_SOME_TEST R8STO_PRINT_SOME prints some of an R8STO matrix. Matrix order N = 5 Rows 2:5, Cols 1:3 Col: 1 2 3 Row --- 2 12 11 12 3 13 12 11 4 14 13 12 5 15 14 13 R8STO_RANDOM_TEST R8STO_RANDOM randomizes an R8STO matrix. Matrix order N = 5 The R8STO matrix: Col: 1 2 3 4 5 Row --- 1 0.218418 0.956318 0.829509 0.561695 0.415307 2 0.956318 0.218418 0.956318 0.829509 0.561695 3 0.829509 0.956318 0.218418 0.956318 0.829509 4 0.561695 0.829509 0.956318 0.218418 0.956318 5 0.415307 0.561695 0.829509 0.956318 0.218418 R8STO_SL_TEST R8STO_SL solves a positive definite symmetric Toeplitz system. Matrix order N = 5 The symmetric Toeplitz matrix A: Col: 1 2 3 4 5 Row --- 1 1 0.5 0.2 0.1 0.05 2 0.5 1 0.5 0.2 0.1 3 0.2 0.5 1 0.5 0.2 4 0.1 0.2 0.5 1 0.5 5 0.05 0.1 0.2 0.5 1 The right hand side vector B: 1: 0.629447 2: 0.811584 3: -0.746026 4: 0.826752 5: 0.264718 The solution X: 1: 0.133622 2: 1.63501 3: -2.46879 4: 1.90218 5: -0.362796 Norm of residual error A * X - B = 4.742875e-16 R8STO_TO_R8GE_TEST R8STO_TO_R8GE converts a matrix from R8STO to R8GE format. Matrix order N = 5 The R8STO matrix: Col: 1 2 3 4 5 Row --- 1 0.218418 0.956318 0.829509 0.561695 0.415307 2 0.956318 0.218418 0.956318 0.829509 0.561695 3 0.829509 0.956318 0.218418 0.956318 0.829509 4 0.561695 0.829509 0.956318 0.218418 0.956318 5 0.415307 0.561695 0.829509 0.956318 0.218418 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 0.218418 0.956318 0.829509 0.561695 0.415307 2 0.956318 0.218418 0.956318 0.829509 0.561695 3 0.829509 0.956318 0.218418 0.956318 0.829509 4 0.561695 0.829509 0.956318 0.218418 0.956318 5 0.415307 0.561695 0.829509 0.956318 0.218418 R8STO_YW_SL_TEST R8STO_YW_SL solves the Yule-Walker equations for a symmetric Toeplitz system. Matrix order N = 5 The symmetric Toeplitz matrix A: Col: 1 2 3 4 5 Row --- 1 1 0.5 0.2 0.1 0.05 2 0.5 1 0.5 0.2 0.1 3 0.2 0.5 1 0.5 0.2 4 0.1 0.2 0.5 1 0.5 5 0.05 0.1 0.2 0.5 1 The right hand side, B: 1: -0.5 2: -0.2 3: -0.1 4: -0.05 5: -0.02 The computed solution, X: 1: -0.535896 2: 0.0860477 3: -0.0384393 4: 0.00354769 5: 0.00410405 The residual A*X - B: 1: 0 2: 0 3: 0 4: 0 5: 3.46945e-18 R8STO_ZEROS_TEST R8STO_ZEROS zeros an R8STO matrix. Matrix order N = 5 The R8STO matrix: Col: 1 2 3 4 5 Row --- 1 0 0 0 0 0 2 0 0 0 0 0 3 0 0 0 0 0 4 0 0 0 0 0 5 0 0 0 0 0 r8sto_test(): Normal end of execution. 28-Aug-2022 10:16:40