Wed Oct 8 08:50:33 2025 r8po_test(): python version: 3.10.12 numpy version: 1.26.4 Test r8po(). r8ge_to_r8po_test(): r8ge_to_r8po() converts an R8GE matrix to R8PO format. Matrix order N = 5 The random R8GE matrix: [[0.72283481 0.2912815 0.2606277 0.62085789 0.29577451] [0.24281767 0.68175543 0.25172033 0.27612521 0.82171848] [0.70767037 0.13920248 0.45992108 0.8665237 0.66175998] [0.13902264 0.41214754 0.72845905 0.28228461 0.61722601] [0.23178086 0.25353039 0.16098341 0.09289134 0.11667668]] The R8PO matrix: [[0.72283481 0.2912815 0.2606277 0.62085789 0.29577451] [0. 0.68175543 0.25172033 0.27612521 0.82171848] [0. 0. 0.45992108 0.8665237 0.66175998] [0. 0. 0. 0.28228461 0.61722601] [0. 0. 0. 0. 0.11667668]] R8PO_DET_TEST R8PO_DET finds the determinant of a positive definite symmetric matrix after it has been factored. Matrix order N = 5 The matrix A: Col: 0 1 2 3 4 Row 0 : 1 1 1 1 1 1 : 1 2 2 2 2 2 : 1 2 3 3 3 3 : 1 2 3 4 4 4 : 1 2 3 4 5 Determinant of A = 1.0 R8PO_DIF2_TEST R8PO_DIF2 returns the second difference matrix in R8PO format. 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 R8PO_FA_TEST R8PO_FA factors a positive definite symmetric linear system, Matrix order N = 5 The matrix A: Col: 0 1 2 3 4 Row 0 : 1 1 1 1 1 1 : 1 2 2 2 2 2 : 1 2 3 3 3 3 : 1 2 3 4 4 4 : 1 2 3 4 5 The factor R (a R8UT matrix): [[1. 1. 1. 1. 1.] [0. 1. 1. 1. 1.] [0. 0. 1. 1. 1.] [0. 0. 0. 1. 1.] [0. 0. 0. 0. 1.]] The product R' * R: [[1. 1. 1. 1. 1.] [1. 2. 2. 2. 2.] [1. 2. 3. 3. 3.] [1. 2. 3. 4. 4.] [1. 2. 3. 4. 5.]] r8po_indicator_test r8po_indicator sets up an R8PO indicator matrix. Matrix order N = 5 The R8PO indicator matrix: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 12 22 23 24 25 2 : 13 23 33 34 35 3 : 14 24 34 44 45 4 : 15 25 35 45 55 r8po_inverse_test r8po_inverse computes the inverse of a symmetric positive definite matrix factored by R8PO_FA. Matrix order N = 4 Matrix A: Col: 0 1 2 3 Row 0 : 1 1 1 1 1 : 1 2 2 2 2 : 1 2 3 3 3 : 1 2 3 4 Inverse matrix B: Col: 0 1 2 3 Row 0 : 2 -1 0 -0 1 : -1 2 -1 -0 2 : 0 -1 2 -1 3 : -0 -0 -1 1 Product A * B: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 1 0 3 : 0 0 0 1 R8PO_ML_TEST R8PO_ML can compute A*x for an R8PO matrix A even after it has been factored by R8PO_FA. Solution: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 Solution: 0: 1 1: 1 2: 1 3: 1 4: 1 5: 1 6: 1 7: 1 8: 1 9: 1 r8po_mm_test r8po_mm computes the product of two symmetric positive definite matrices. Matrix order N = 5 Matrix A: 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 Matrix B: Col: 0 1 2 3 4 Row 0 : 1 2 0 0 0 1 : 2 3 4 0 0 2 : 0 4 5 6 0 3 : 0 0 6 7 8 4 : 0 0 0 8 9 Product matrix C = A * B: Col: 0 1 2 3 4 Row 0 : 0 1 -4 0 0 1 : 1 0 3 -6 0 2 : -4 3 0 5 -8 3 : 0 -6 5 0 7 4 : 0 0 -8 7 10 R8PO_MV_TEST R8PO_MV computes the product of an R8PO matrix and a vector. Matrix order N = 5 Matrix A: 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 Vector V: 0: 1 1: 2 2: 3 3: 4 4: 5 Product w = A * v: 0: 0 1: 0 2: 0 3: 0 4: 6 r8po_print_test r8po_print prints an R8PO matrix. Here is an R8PO matrix: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 12 22 23 24 25 2 : 13 23 33 34 35 3 : 14 24 34 44 45 4 : 15 25 35 45 55 R8PO_PRINT_SOME_TEST R8PO_PRINT_SOME prints some of an R8PO matrix. Here is an R8PO matrix: Col: 3 4 Row 0 : 14 15 1 : 24 25 2 : 34 35 3 : 44 45 r8po_random_test(): r8po_random() computes a random positive definite symmetric matrix. Matrix order N = 5 The random R8PO matrix: Col: 0 1 2 3 4 Row 0 : 0.00903018 0.0344301 0.0310878 0.0265154 0.0841396 1 : 0.0344301 0.954408 0.449456 0.630451 0.720869 2 : 0.0310878 0.449456 0.241245 0.338395 0.466732 3 : 0.0265154 0.630451 0.338395 1.84158 1.0851 4 : 0.0841396 0.720869 0.466732 1.0851 1.62072 R8PO_SL_TEST R8PO_SL solves a linear system with an R8PO matrix after it has been factored by R8PO_FA. Matrix order N = 5 Matrix A: 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 Right hand side b: 0: 0 1: 0 2: 0 3: 0 4: 6 Solution x: 0: 1 1: 2 2: 3 3: 4 4: 5 r8po_to_r8ge_test(): r8po_to_r8ge() converts a R8PO matrix to R8GE format. Matrix order N = 5 The random R8PO matrix: Col: 0 1 2 3 4 Row 0 : 0.237386 0.445288 0.446161 0.204439 0.154742 1 : 0.445288 1.13489 1.21149 0.786716 0.533499 2 : 0.446161 1.21149 2.15956 1.53439 1.39242 3 : 0.204439 0.786716 1.53439 1.23068 1.0818 4 : 0.154742 0.533499 1.39242 1.0818 1.1397 The random R8GE matrix: [[0.23738591 0.44528761 0.44616144 0.20443851 0.15474164] [0.44528761 1.13488526 1.21149254 0.7867158 0.53349853] [0.44616144 1.21149254 2.15956159 1.53439018 1.39242274] [0.20443851 0.7867158 1.53439018 1.23068217 1.081801 ] [0.15474164 0.53349853 1.39242274 1.081801 1.13969829]] r8po_zeros_test r8po_zeros zeros out space for a symmetric positive definite matrix. Matrix order N = 5 Matrix A: 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 r8po_test(): Normal end of execution. Wed Oct 8 08:50:34 2025