Wed Oct 8 08:50:35 2025 r8sto_test(): python version: 3.10.12 numpy version: 1.26.4 Test r8sto(). r8sto_dif2_test(): r8sto_dif2() sets up a R8STO second difference matrix. 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 : 0.975941 0.0212051 0.248101 0.342038 0.256454 1 : 0.0212051 0.975941 0.0212051 0.248101 0.342038 2 : 0.248101 0.0212051 0.975941 0.0212051 0.248101 3 : 0.342038 0.248101 0.0212051 0.975941 0.0212051 4 : 0.256454 0.342038 0.248101 0.0212051 0.975941 x: 0: 1 1: 2 2: 3 3: 4 4: 5 b=A*x: 0: 4.41307 1: 4.73929 2: 4.54366 3: 4.91164 4: 6.64935 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 : 0.370234 0.221435 0.766826 0.350782 0.117178 1 : 0.221435 0.370234 0.221435 0.766826 0.350782 2 : 0.766826 0.221435 0.370234 0.221435 0.766826 3 : 0.350782 0.766826 0.221435 0.370234 0.221435 4 : 0.117178 0.350782 0.766826 0.221435 0.370234 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 : 0.346029 0.326237 0.45454 0.432417 0.438752 1 : 0.326237 0.346029 0.326237 0.45454 0.432417 2 : 0.45454 0.326237 0.346029 0.326237 0.45454 3 : 0.432417 0.45454 0.326237 0.346029 0.326237 4 : 0.438752 0.432417 0.45454 0.326237 0.346029 The R8GE matrix: [[0.34602851 0.32623726 0.45453963 0.43241673 0.43875244] [0.32623726 0.34602851 0.32623726 0.45453963 0.43241673] [0.45453963 0.32623726 0.34602851 0.32623726 0.45453963] [0.43241673 0.45453963 0.32623726 0.34602851 0.32623726] [0.43875244 0.43241673 0.45453963 0.32623726 0.34602851]] 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. Wed Oct 8 08:50:35 2025