06 October 2025 6:33:36.711 PM r8po_test(): Fortran90 version: Test r8po(). R8GE_TO_R8PO_TEST R8GE_TO_R8PO converts an R8GE matrix to R8PO format. Matrix order N = 5 The random R8GE matrix A: Col: 1 2 3 4 5 Row --- 1 0.165700 0.996876 0.917743 0.881647 0.977552 2 0.491518 0.714117 0.176086 0.834001 0.369153E-01 3 0.629915 0.268427 0.953478 0.671709 0.586293 4 0.282441 0.963572 0.455445 0.494724 0.202918 5 0.378257 0.137644 0.162834 0.701080 0.700360 The R8PO matrix Col: 1 2 3 4 5 Row --- 1 0.165700 0.996876 0.917743 0.881647 0.977552 2 0.996876 0.714117 0.176086 0.834001 0.369153E-01 3 0.917743 0.176086 0.953478 0.671709 0.586293 4 0.881647 0.834001 0.671709 0.494724 0.202918 5 0.977552 0.369153E-01 0.586293 0.202918 0.700360 R8PO_DET_TEST R8PO_DET computes the determinant of a symmetric positive definite matrix factored by R8PO_FA,. Matrix order N = 4 Matrix A: Col: 1 2 3 4 Row --- 1 2.00000 -1.00000 0.00000 0.00000 2 -1.00000 2.00000 -1.00000 0.00000 3 0.00000 -1.00000 2.00000 -1.00000 4 0.00000 0.00000 -1.00000 2.00000 Determinant of A = 5.00000 R8PO_DIF2_TEST R8PO_DIF2 sets the second difference matrix in R8PO format. The R8PO DIF2 matrix: Col: 1 2 3 4 5 Row --- 1 2.00000 -1.00000 0.00000 0.00000 0.00000 2 -1.00000 2.00000 -1.00000 0.00000 0.00000 3 0.00000 -1.00000 2.00000 -1.00000 0.00000 4 0.00000 0.00000 -1.00000 2.00000 -1.00000 5 0.00000 0.00000 0.00000 -1.00000 2.00000 R8PO_FA_TEST R8PO_FA factors a positive definite symmetric linear system, Matrix order N = 5 The matrix A: Col: 1 2 3 4 5 Row --- 1 1.00000 1.00000 1.00000 1.00000 1.00000 2 1.00000 2.00000 2.00000 2.00000 2.00000 3 1.00000 2.00000 3.00000 3.00000 3.00000 4 1.00000 2.00000 3.00000 4.00000 4.00000 5 1.00000 2.00000 3.00000 4.00000 5.00000 The factor R (an R8UT matrix): Col: 1 2 3 4 5 Row --- 1 1.00000 1.00000 1.00000 1.00000 1.00000 2 1.00000 1.00000 1.00000 1.00000 3 1.00000 1.00000 1.00000 4 1.00000 1.00000 5 1.00000 The product R' * R: Col: 1 2 3 4 5 Row --- 1 1.00000 1.00000 1.00000 1.00000 1.00000 2 1.00000 2.00000 2.00000 2.00000 2.00000 3 1.00000 2.00000 3.00000 3.00000 3.00000 4 1.00000 2.00000 3.00000 4.00000 4.00000 5 1.00000 2.00000 3.00000 4.00000 5.00000 R8PO_INDICATOR_TEST R8PO_INDICATOR sets up an R8PO indicator matrix. Matrix order N = 5 The R8PO indicator matrix: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 13.0000 14.0000 15.0000 2 12.0000 22.0000 23.0000 24.0000 25.0000 3 13.0000 23.0000 33.0000 34.0000 35.0000 4 14.0000 24.0000 34.0000 44.0000 45.0000 5 15.0000 25.0000 35.0000 45.0000 55.0000 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: 1 2 3 4 Row --- 1 1.00000 1.00000 1.00000 1.00000 2 1.00000 2.00000 2.00000 2.00000 3 1.00000 2.00000 3.00000 3.00000 4 1.00000 2.00000 3.00000 4.00000 Inverse matrix B: Col: 1 2 3 4 Row --- 1 2.00000 -1.00000 0.00000 -0.00000 2 -1.00000 2.00000 -1.00000 -0.00000 3 0.00000 -1.00000 2.00000 -1.00000 4 -0.00000 -0.00000 -1.00000 1.00000 Product A * B: Col: 1 2 3 4 Row --- 1 1.00000 0.00000 0.00000 0.00000 2 0.00000 1.00000 0.00000 0.00000 3 0.00000 0.00000 1.00000 0.00000 4 0.00000 0.00000 0.00000 1.00000 R8PO_ML_TEST R8PO_ML can compute A*x for an R8PO matrix A even after it has been factored by R8PO_FA. Solution: 1: 1.0000000 2: 2.0000000 3: 3.0000000 4: 4.0000000 5: 5.0000000 6: 6.0000000 7: 7.0000000 8: 8.0000000 9: 9.0000000 10: 10.000000 Solution: 1: 1.0000000 2: 1.0000000 3: 1.0000000 4: 1.0000000 5: 1.0000000 6: 1.0000000 7: 1.0000000 8: 1.0000000 9: 1.0000000 10: 1.0000000 R8PO_MM_TEST R8PO_MM computes the product of two symmetric positive definite matrices. Matrix order N = 5 Matrix A: Col: 1 2 3 4 5 Row --- 1 2.00000 -1.00000 0.00000 0.00000 0.00000 2 -1.00000 2.00000 -1.00000 0.00000 0.00000 3 0.00000 -1.00000 2.00000 -1.00000 0.00000 4 0.00000 0.00000 -1.00000 2.00000 -1.00000 5 0.00000 0.00000 0.00000 -1.00000 2.00000 Matrix B: Col: 1 2 3 4 5 Row --- 1 1.00000 2.00000 0.00000 0.00000 0.00000 2 2.00000 3.00000 4.00000 0.00000 0.00000 3 0.00000 4.00000 5.00000 6.00000 0.00000 4 0.00000 0.00000 6.00000 7.00000 8.00000 5 0.00000 0.00000 0.00000 8.00000 9.00000 Product matrix C = A * B: Col: 1 2 3 4 5 Row --- 1 0.00000 1.00000 -4.00000 0.00000 0.00000 2 1.00000 0.00000 3.00000 -6.00000 0.00000 3 -4.00000 3.00000 0.00000 5.00000 -8.00000 4 0.00000 -6.00000 5.00000 0.00000 7.00000 5 0.00000 0.00000 -8.00000 7.00000 10.0000 R8PO_MV_TEST R8PO_MV computes the product of a symmetric positive definite matrix times a vector. Matrix order N = 5 Matrix A: Col: 1 2 3 4 5 Row --- 1 2.00000 -1.00000 0.00000 0.00000 0.00000 2 -1.00000 2.00000 -1.00000 0.00000 0.00000 3 0.00000 -1.00000 2.00000 -1.00000 0.00000 4 0.00000 0.00000 -1.00000 2.00000 -1.00000 5 0.00000 0.00000 0.00000 -1.00000 2.00000 Vector V: 1: 1.0000000 2: 2.0000000 3: 3.0000000 4: 4.0000000 5: 5.0000000 Product w = A * v: 1: 0.0000000 2: 0.0000000 3: 0.0000000 4: 0.0000000 5: 6.0000000 R8PO_PRINT_TEST R8PO_PRINT prints an R8PO matrix. The R8PO matrix: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 13.0000 14.0000 15.0000 2 12.0000 22.0000 23.0000 24.0000 25.0000 3 13.0000 23.0000 33.0000 34.0000 35.0000 4 14.0000 24.0000 34.0000 44.0000 45.0000 5 15.0000 25.0000 35.0000 45.0000 55.0000 R8PO_PRINT_SOME_TEST R8PO_PRINT_SOME prints some of an R8PO matrix. Rows 2-6, Columns 5-7: Col: 5 6 7 Row --- 2 205.000 206.000 207.000 3 305.000 306.000 307.000 4 405.000 406.000 407.000 5 505.000 506.000 507.000 6 506.000 606.000 607.000 R8PO_RANDOM_TEST R8PO_RANDOM computes a random positive definite symmetric matrix. Matrix order N = 5 The random R8PO matrix: Col: 1 2 3 4 5 Row --- 1 0.315004E-01 0.172230 0.113263 0.129225 0.105298 2 0.172230 0.941866 0.630236 0.711383 0.583002 3 0.113263 0.630236 1.07347 0.790570 0.854023 4 0.129225 0.711383 0.790570 1.17379 1.24819 5 0.105298 0.583002 0.854023 1.24819 1.97613 R8PO_SL_TEST R8PO_SL solves a linear system with R8PO matrix after it has been factored buy R8PO_FA. Matrix order N = 5 Matrix A: Col: 1 2 3 4 5 Row --- 1 2.00000 -1.00000 0.00000 0.00000 0.00000 2 -1.00000 2.00000 -1.00000 0.00000 0.00000 3 0.00000 -1.00000 2.00000 -1.00000 0.00000 4 0.00000 0.00000 -1.00000 2.00000 -1.00000 5 0.00000 0.00000 0.00000 -1.00000 2.00000 Right hand side b: 1: 0.0000000 2: 0.0000000 3: 0.0000000 4: 0.0000000 5: 6.0000000 Solution vector X: 1: 1.0000000 2: 2.0000000 3: 3.0000000 4: 4.0000000 5: 5.0000000 R8PO_TO_R8GE_TEST R8PO_TO_R8GE converts an R8PO matrix to R8GE format. Matrix order N = 5 The random R8PO matrix A: Col: 1 2 3 4 5 Row --- 1 0.801254 0.817735 0.553436 0.440602 0.939256E-01 2 0.817735 0.962367 0.647516 0.714239 0.138879 3 0.553436 0.647516 0.926412 1.17477 0.494313 4 0.440602 0.714239 1.17477 1.89829 0.766882 5 0.939256E-01 0.138879 0.494313 0.766882 0.523138 The random R8PO matrix (printed by R8GE_PRINT): Col: 1 2 3 4 5 Row --- 1 0.801254 0.817735 0.553436 0.440602 0.939256E-01 2 0.00000 0.962367 0.647516 0.714239 0.138879 3 0.00000 0.00000 0.926412 1.17477 0.494313 4 0.00000 0.00000 0.00000 1.89829 0.766882 5 0.00000 0.00000 0.00000 0.00000 0.523138 The random R8GE matrix (printed by R8GE_PRINT): Col: 1 2 3 4 5 Row --- 1 0.801254 0.817735 0.553436 0.440602 0.939256E-01 2 0.817735 0.962367 0.647516 0.714239 0.138879 3 0.553436 0.647516 0.926412 1.17477 0.494313 4 0.440602 0.714239 1.17477 1.89829 0.766882 5 0.939256E-01 0.138879 0.494313 0.766882 0.523138 R8PO_ZEROS_TEST R8PO_ZEROS zeros out a matrix in R8PO format. Matrix order N = 5 The zero R8PO matrix: Col: 1 2 3 4 5 Row --- 1 0.00000 0.00000 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 0.00000 0.00000 5 0.00000 0.00000 0.00000 0.00000 0.00000 r8po_test(): Normal end of execution. 06 October 2025 6:33:36.712 PM