Thu Aug 25 18:33:45 2022 r8po_test(): Python version: 3.6.9 Test r8po(). r8ge_to_r8po_test(): r8ge_to_r8po() converts an R8GE matrix to R8PO format. Matrix order N = 5 The random R8GE matrix: [[0.93473883 0.048237 0.69919114 0.15302594 0.29222755] [0.26042485 0.89031359 0.8827103 0.92373004 0.8241085 ] [0.3001791 0.59817551 0.13242837 0.79067296 0.7411722 ] [0.58899798 0.17354592 0.66184985 0.10214599 0.02179171] [0.28619066 0.68458087 0.75398807 0.96754914 0.37385531]] The R8PO matrix: [[0.93473883 0.048237 0.69919114 0.15302594 0.29222755] [0. 0.89031359 0.8827103 0.92373004 0.8241085 ] [0. 0. 0.13242837 0.79067296 0.7411722 ] [0. 0. 0. 0.10214599 0.02179171] [0. 0. 0. 0. 0.37385531]] 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 : 0.437555 0.00693239 0.295052 0.565422 0.206418 1 : 0.00693239 0.00187529 0.0446255 0.0232609 0.0138566 2 : 0.295052 0.0446255 1.80407 0.853474 0.733044 3 : 0.565422 0.0232609 0.853474 0.884119 0.470893 4 : 0.206418 0.0138566 0.733044 0.470893 1.40677 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 : 0.553874 0.1987 0.360705 0.73757 0.502251 1 : 0.1987 0.694811 0.214286 0.347393 0.532988 2 : 0.360705 0.214286 0.64453 0.79872 0.501419 3 : 0.73757 0.347393 0.79872 1.7995 1.41175 4 : 0.502251 0.532988 0.501419 1.41175 1.90636 The random R8GE matrix: [[0.55387409 0.19870018 0.36070535 0.73757037 0.50225104] [0.19870018 0.69481104 0.21428639 0.34739347 0.53298804] [0.36070535 0.21428639 0.64453023 0.79872004 0.50141919] [0.73757037 0.34739347 0.79872004 1.79949741 1.41174744] [0.50225104 0.53298804 0.50141919 1.41174744 1.90636214]] 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. Thu Aug 25 18:33:45 2022