Tue May 20 22:27:34 2025 r8ge_test(): python version: 3.10.12 numpy version: 1.26.4 Test r8ge(). i4_log_10_test(): i4_log_10(): whole part of log base 10, X, i4_log_10 0 0 1 0 2 0 3 0 9 0 10 1 11 1 99 1 101 2 -1 0 -2 0 -3 0 -9 0 r8_sign_test(): r8_sign returns the sign of an R8. R8 r8_sign(R8) -1.2500 -1 -0.2500 -1 0.0000 1 0.5000 1 9.0000 1 r8ge_cg_test(): r8ge_cg() applies CG to an R8GE matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 4.52822e-16 Norm of error ||x1-x2|| = 3.30186e-15 r8ge_co_test(): r8ge_co estimates the condition number of an R8GE matrix. Matrix order N = 4 The L1 condition number is 10 The r8ge_co estimate is 7 r8ge_det_test(): r8ge_det computes the determinant of an R8GE matrix. r8ge_det computes the determinant = 112.0 Exact determinant = 112.0 r8ge_dif2_test(): r8ge_dif2 returns the second difference matrix. DIF2 matrix: 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 2 4 : 0 0 0 -1 r8ge_dilu_test(): r8ge_dilu returns the DILU factors of an R8GE matrix. Matrix rows M = 9 Matrix columns N = 9 Matrix A: Col: 0 1 2 3 4 Row 0 : 4 -1 0 -1 0 1 : -1 4 -1 0 -1 2 : 0 -1 4 -1 0 3 : -1 0 -1 4 -1 4 : 0 -1 0 -1 4 5 : 0 0 -1 0 -1 6 : 0 0 0 -1 0 7 : 0 0 0 0 -1 8 : 0 0 0 0 0 Col: 5 6 7 8 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : -1 0 0 0 3 : 0 -1 0 0 4 : -1 0 -1 0 5 : 4 -1 0 -1 6 : -1 4 -1 0 7 : 0 -1 4 -1 8 : -1 0 -1 4 DILU factor: 0: 0.25 1: 0.266667 2: 0.267857 3: 0.287179 4: 0.290179 5: 0.290532 6: 0.292202 7: 0.292601 8: 0.292666 r8ge_fa_test01() r8ge_fa() computes the LU factors of an R8GE matrix, r8ge_sl() solves a factored R8GE system. Matrix order N = 10 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 Solution of transposed system: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 r8ge_fa_test02(): r8ge_fa() computes the LU factors of an R8GE system, r8ge_sl() solves a factored R8GE system. Matrix order N = 5 The matrix: Col: 0 1 2 3 4 Row 0 : 0.826566 0.398321 0.490377 0.420006 0.0957848 1 : 0.447555 0.106998 0.242568 0.738551 0.0973993 2 : 0.272152 0.303541 0.336086 0.580059 0.116672 3 : 0.53553 0.185286 0.203638 0.99535 0.538329 4 : 0.869527 0.570747 0.320628 0.759238 0.346173 The compressed LU factors: Col: 0 1 2 3 4 Row 0 : 0.869527 0.570747 0.320628 0.759238 0.346173 1 : -0.514711 -0.186771 0.0775373 0.347762 -0.0807796 2 : -0.312988 0.668752 0.287587 0.574993 -0.0456972 3 : -0.615887 -0.890014 0.218516 -0.821616 -0.15093 4 : -0.950592 -0.772207 -0.437139 0.418537 0.323866 The pivot vector P: 0 4 1 1 2 2 3 4 4 4 Solution: 0: 1 1: 2 2: 3 3: 4 4: 5 r8ge_fs_test(): r8ge_fs() factors and solves a linear system involving an R8GE matrix. Matrix order N = 10 Solution: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 r8ge_fss_test(): r8ge_fss() factors and solves multiple linear systems associated with an R8GE matrix. Matrix order N = 10 Solution: Col: 0 1 2 Row 0 : 1 1 1 1 : 1 2 2 2 : 1 3 3 3 : 1 4 1 4 : 1 5 2 5 : 1 6 3 6 : 1 7 1 7 : 1 8 2 8 : 1 9 3 9 : 1 10 1 r8ge_hilbert_test(): r8ge_hilbert returns the Hilbert matrix. Hilbert matrix: Col: 0 1 2 3 Row 0 : 1 0.5 0.333333 0.25 1 : 0.5 0.333333 0.25 0.2 2 : 0.333333 0.25 0.2 0.166667 3 : 0.25 0.2 0.166667 0.142857 4 : 0.2 0.166667 0.142857 0.125 r8ge_hilbert_inverse_test(): r8ge_hilbert_inverse() computes the inverse of the Hilbert matrix, stored as an R8GE matrix. Matrix order N = 4 Matrix A: Col: 0 1 2 3 Row 0 : 1 0.5 0.333333 0.25 1 : 0.5 0.333333 0.25 0.2 2 : 0.333333 0.25 0.2 0.166667 3 : 0.25 0.2 0.166667 0.142857 Inverse matrix B: Col: 0 1 2 3 Row 0 : 16 -120 240 -140 1 : -120 1200 -2700 1680 2 : 240 -2700 6480 -4200 3 : -140 1680 -4200 2800 Product A * B: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 1 -5.68434e-14 3 : 0 0 0 1 r8ge_house_axh_test(): r8ge_house_axh() multiplies a matrix A times a compact Householder matrix. Matrix A: Col: 0 1 2 3 4 Row 0 : -4.74372 -1.80772 0.920938 0.848763 2.72911 1 : -0.215457 1.36672 -2.95132 -2.59129 -3.38964 2 : -3.94771 -4.60042 3.45525 -2.21482 4.03023 3 : 3.9025 -0.732314 0.819332 -3.75868 4.43761 4 : -1.92665 1.09698 -0.110159 -2.18651 0.450058 Compact vector V so column 3 of H*A is packed: 0: 0 1: 0 2: 0.993114 3: 0.116108 4: -0.0156108 Householder matrix H: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : 0 1 0 0 0 2 : 0 0 -0.97255 -0.230618 0.0310065 3 : 0 0 -0.230618 0.973038 0.00362509 4 : 0 0 0.0310065 0.00362509 0.999513 Indirect product A*H: Col: 0 1 2 3 4 Row 0 : -4.74372 -1.80772 -1.00678 0.623387 2.75941 1 : -0.215457 1.36672 3.36281 -1.85309 -3.48889 2 : -3.94771 -4.60042 -2.72466 -2.93733 4.12737 3 : 3.9025 -0.732314 0.207572 -3.8302 4.44722 4 : -1.92665 1.09698 0.625339 -2.10052 0.438497 Direct product A*H: Col: 0 1 2 3 4 Row 0 : -4.74372 -1.80772 -1.00678 0.623387 2.75941 1 : -0.215457 1.36672 3.36281 -1.85309 -3.48889 2 : -3.94771 -4.60042 -2.72466 -2.93733 4.12737 3 : 3.9025 -0.732314 0.207572 -3.8302 4.44722 4 : -1.92665 1.09698 0.625339 -2.10052 0.438497 H*A should pack column 3: Col: 0 1 2 3 4 Row 0 : -4.74372 -1.80772 0.920938 0.848763 2.72911 1 : -0.215457 1.36672 -2.95132 -2.59129 -3.38964 2 : 2.87962 4.67704 -3.55277 2.95304 -4.92904 3 : 4.70071 0.352347 -7.91468e-17 -3.15449 3.39015 4 : -2.03397 0.951147 2.77556e-17 -2.26775 0.590889 r8ge_house_form_test(): r8ge_house_form forms a Householder matrix from its compact form. Compact vector form V: 0: 0 1: 0 2: 1 3: 2 4: 3 Householder matrix H: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : 0 1 0 0 0 2 : 0 0 0.857143 -0.285714 -0.428571 3 : 0 0 -0.285714 0.428571 -0.857143 4 : 0 0 -0.428571 -0.857143 -0.285714 r8ge_identity_test(): r8ge_identity returns the identity matrix. Identity matrix: 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 4 : 0 0 0 0 r8ge_ilu_test(): r8ge_ilu returns the ILU factors of an R8GE matrix. Matrix rows M = 9 Matrix columns N = 9 Matrix A: Col: 0 1 2 3 4 Row 0 : 4 -1 0 -1 0 1 : -1 4 -1 0 -1 2 : 0 -1 4 -1 0 3 : -1 0 -1 4 -1 4 : 0 -1 0 -1 4 5 : 0 0 -1 0 -1 6 : 0 0 0 -1 0 7 : 0 0 0 0 -1 8 : 0 0 0 0 0 Col: 5 6 7 8 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : -1 0 0 0 3 : 0 -1 0 0 4 : -1 0 -1 0 5 : 4 -1 0 -1 6 : -1 4 -1 0 7 : 0 -1 4 -1 8 : -1 0 -1 4 Factor L: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : -0.25 1 0 0 0 2 : 0 -0.266667 1 0 0 3 : -0.25 0 -0.267857 1 0 4 : 0 -0.266667 0 -0.287179 1 5 : 0 0 -0.267857 0 -0.290179 6 : 0 0 0 -0.287179 0 7 : 0 0 0 0 -0.290179 8 : 0 0 0 0 0 Col: 5 6 7 8 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : 0 0 0 0 3 : 0 0 0 0 4 : 0 0 0 0 5 : 1 0 0 0 6 : -0.290532 1 0 0 7 : 0 -0.292202 1 0 8 : -0.290532 0 -0.292601 1 Factor U: Col: 0 1 2 3 4 Row 0 : 4 -1 0 -1 0 1 : 0 3.75 -1 0 -1 2 : 0 0 3.73333 -1 0 3 : 0 0 0 3.48214 -1 4 : 0 0 0 0 3.44615 5 : 0 0 0 0 0 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 Col: 5 6 7 8 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : -1 0 0 0 3 : 0 -1 0 0 4 : -1 0 -1 0 5 : 3.44196 -1 0 -1 6 : 0 3.42229 -1 0 7 : 0 0 3.41762 -1 8 : 0 0 0 3.41687 Product L*U: Col: 0 1 2 3 4 Row 0 : 4 -1 0 -1 0 1 : -1 4 -1 0.25 -1 2 : 0 -1 4 -1 0.266667 3 : -1 0.25 -1 4 -1 4 : 0 -1 0.266667 -1 4 5 : 0 0 -1 0.267857 -1 6 : 0 0 0 -1 0.287179 7 : 0 0 0 0 -1 8 : 0 0 0 0 0 Col: 5 6 7 8 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : -1 0 0 0 3 : 0.267857 -1 0 0 4 : -1 0.287179 -1 0 5 : 4 -1 0.290179 -1 6 : -1 4 -1 0.290532 7 : 0.290179 -1 4 -1 8 : -1 0.290532 -1 4 r8ge_indicator_test(): r8ge_indicator returns the indicator matrix. Indicator matrix: Col: 0 1 2 3 Row 0 : 11 12 13 14 1 : 21 22 23 24 2 : 31 32 33 34 3 : 41 42 43 44 4 : 51 52 53 54 r8ge_inverse_test(): r8ge_inverse computes the inverse of an R8GE matrix. Matrix order N = 4 Matrix A: Col: 0 1 2 3 Row 0 : 5 3 3 3 1 : 3 5 3 3 2 : 3 3 5 3 3 : 3 3 3 5 Inverse matrix B: Col: 0 1 2 3 Row 0 : 0.392857 -0.107143 -0.107143 -0.107143 1 : -0.107143 0.392857 -0.107143 -0.107143 2 : -0.107143 -0.107143 0.392857 -0.107143 3 : -0.107143 -0.107143 -0.107143 0.392857 Product matrix: Col: 0 1 2 3 Row 0 : 1 -1.11022e-16 0 0 1 : 3.33067e-16 1 0 0 2 : 4.44089e-16 -1.11022e-16 1 2.22045e-16 3 : 4.44089e-16 -1.11022e-16 0 1 r8ge_ml_test(): r8ge_ml() computes A*x or A'*X where A has been factored by r8ge_fa. Matrix order N = 10 A*x and PLU*x 0: 34.3034 34.3034 1: 26.4588 26.4588 2: 41.6573 41.6573 3: 29.1498 29.1498 4: 25.6423 25.6423 5: 24.1145 24.1145 6: 28.3556 28.3556 7: 30.9089 30.9089 8: 28.8585 28.8585 9: 24.7179 24.7179 A'*x and (PLU)'*x 0: 32.1234 32.1234 1: 29.7754 29.7754 2: 30.3883 30.3883 3: 21.0874 21.0874 4: 22.1183 22.1183 5: 27.6894 27.6894 6: 19.0104 19.0104 7: 25.8231 25.8231 8: 26.0962 26.0962 9: 16.2545 16.2545 r8ge_mm_test(): r8ge_mm computes a matrix-matrix product C = A * B; A: Col: 0 1 2 Row 0 : 1 0 0 1 : 1 1 0 2 : 1 2 1 3 : 1 3 3 B: Col: 0 1 2 3 Row 0 : 1 1 1 1 1 : 0 1 2 3 2 : 0 0 1 3 C = A*B: Col: 0 1 2 3 Row 0 : 1 1 1 1 1 : 1 2 3 4 2 : 1 3 6 10 3 : 1 4 10 19 r8ge_mtm_test(): r8ge_mtm computes a matrix-matrix product C = A' * B; A: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 1 1 0 0 2 : 1 2 1 0 B: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 1 1 0 0 2 : 1 2 1 0 C = A'*B: Col: 0 1 2 3 Row 0 : 3 3 1 0 1 : 3 5 2 0 2 : 1 2 1 0 3 : 0 0 0 0 r8ge_mtv_test(): r8ge_mtv computes a matrix product b=A'*x for an R8GE matrix. The matrix A: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 21 22 23 24 25 2 : 31 32 33 34 35 The vector x: 0: 1 1: 2 2: 3 The vector b=A'*x: 0: 146 1: 152 2: 158 3: 164 4: 170 The matrix A: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 21 22 23 24 25 2 : 31 32 33 34 35 3 : 41 42 43 44 45 4 : 51 52 53 54 55 The vector x: 0: 1 1: 2 2: 3 3: 4 4: 5 The vector b=A'*x: 0: 565 1: 580 2: 595 3: 610 4: 625 The matrix A: Col: 0 1 2 Row 0 : 11 12 13 1 : 21 22 23 2 : 31 32 33 3 : 41 42 43 4 : 51 52 53 The vector x: 0: 1 1: 2 2: 3 3: 4 4: 5 The vector b=A'*x: 0: 565 1: 580 2: 595 r8ge_mu_test(): r8ge_mu() computes A*x or A'*X where A has been factored by r8ge_trf. Matrix rows M = 5 Matrix columns N = 3 A*x and PLU*x 0: 3.33075 3.33075 1: 1.42 1.42 2: 2.84035 2.84035 3: 1.84247 1.84247 4: 4.22335 4.22335 A'*x and (PLU)'*x 0: 4.88968 4.88968 1: 3.59124 3.59124 2: 8.31469 8.31469 Matrix is 3 by 5 A*x and PLU*x 0: 7.88874 7.88874 1: 6.47332 6.47332 2: 11.9155 11.9155 A'*x and (PLU)'*x 0: 3.96657 3.96657 1: 4.81822 4.81822 2: 3.91089 3.91089 3: 4.25539 4.25539 4: 1.14036 1.14036 r8ge_mv_test(): r8ge_mv computes a matrix product b=A*x for an R8GE matrix. The matrix A: Col: 0 1 2 3 Row 0 : 11 12 13 14 1 : 21 22 23 24 2 : 31 32 33 34 3 : 41 42 43 44 4 : 51 52 53 54 The vector X: 0: 1 1: 2 2: 3 3: 4 4: 5 The vector b=A*x: 0: 130 1: 230 2: 330 3: 430 r8ge_orth_random_test(): r8ge_orth_random computes a random orthogonal matrix. orth_random matrix: Col: 0 1 2 3 4 Row 0 : -0.127775 -0.214159 -0.807809 -0.0865765 -0.527029 1 : 0.295598 -0.484327 0.233789 -0.782587 -0.104643 2 : 0.0542725 -0.813526 -0.0697447 0.456426 0.349344 3 : 0.906513 0.114022 -0.0277633 0.30003 -0.272844 4 : 0.267552 0.211514 -0.535866 -0.285867 0.7175 r8ge_spd_random_test(): r8ge_spd_random computes the spd_random matrix. spd_random matrix: Col: 0 1 2 3 4 Row 0 : 0.841507 0.0124888 0.0371599 0.0918867 0.0559793 1 : 0.0124888 0.654655 0.0912092 -0.172516 -0.120682 2 : 0.0371599 0.0912092 0.831126 -0.0708292 -0.00601272 3 : 0.0918867 -0.172516 -0.0708292 0.150357 -0.16669 4 : 0.0559793 -0.120682 -0.00601272 -0.16669 0.753773 r8ge_plu_test(): r8ge_plu() returns the PLU factors of an R8GE matrix. Matrix rows M = 5 Matrix columns N = 4 Matrix A: Col: 0 1 2 3 Row 0 : 0.309241 0.685554 0.552727 0.548602 1 : 0.590656 0.421371 0.216981 0.895563 2 : 0.0143772 0.366554 0.717323 0.747082 3 : 0.46364 0.713272 0.247234 0.925761 4 : 0.57989 0.0969566 0.203793 0.633899 Factor P: Col: 0 1 2 3 4 Row 0 : 0 1 0 0 0 1 : 1 0 0 0 0 2 : 0 0 1 0 0 3 : 0 0 0 0 1 4 : 0 0 0 1 0 Factor L: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : 0.523555 1 0 0 0 2 : 0.0243411 0.766326 1 0 0 3 : 0.981774 -0.681234 0.772017 1 0 4 : 0.784958 0.822712 -0.757231 -0.937966 1 Factor U: Col: 0 1 2 3 Row 0 : 0.590656 0.421371 0.216981 0.895563 1 : 0 0.464943 0.439126 0.0797252 2 : 0 0 0.375527 0.664188 3 : 0 0 0 -0.703794 4 : 0 0 0 0 Product P*L*U: Col: 0 1 2 3 Row 0 : 0.309241 0.685554 0.552727 0.548602 1 : 0.590656 0.421371 0.216981 0.895563 2 : 0.0143772 0.366554 0.717323 0.747082 3 : 0.46364 0.713272 0.247234 0.925761 4 : 0.57989 0.0969566 0.203793 0.633899 r8ge_poly_test(): r8ge_poly computes the characteristic polynomial of an R8GE matrix. Matrix order N = 12 I, P(I), True P(I) 0: 1 1 1: -23 -23 2: 231 231 3: -1330 -1330 4: 4845 4845 5: -11628 -11628 6: 18564 18564 7: -19448 -19448 ...... .............. .............. 12: 1 1 r8ge_print_test(): r8ge_print prints an R8GE matrix. Here is an R8GE: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 21 22 23 24 25 2 : 31 32 33 34 35 3 : 41 42 43 44 45 Col: 5 Row 0 : 16 1 : 26 2 : 36 3 : 46 r8ge_print_some_test(): r8ge_print_some prints some of an R8GE matrix. Rows 0:2, Cols 3:5: Col: 3 4 5 Row 0 : 14 15 16 1 : 24 25 26 2 : 34 35 36 r8ge_random_test(): r8ge_random() computes a random R8GE. 0 <= X <= 1 Random R8GE: Col: 0 1 2 3 Row 0 : 0.63911 0.631378 0.137598 0.462319 1 : 0.496964 0.542255 0.182655 0.699562 2 : 0.174588 0.251352 0.49892 0.162753 3 : 0.618904 0.727279 0.363375 0.769398 4 : 0.283892 0.201948 0.712052 0.42178 r8ge_random_ab_test(): r8ge_random_ab computes a random R8GE. -1 <= X <= 5 Random R8GE: Col: 0 1 2 3 Row 0 : 0.705894 2.57545 2.94525 4.86231 1 : 2.20014 1.67293 1.72863 2.76173 2 : 4.32259 2.7602 1.70664 3.87045 3 : -0.73313 3.395 -0.227091 0.798272 4 : 2.63142 4.86751 3.80589 -0.23287 r8ge_res_test(): r8ge_res computes b-A*x, where A is an R8GE matrix. We check three cases, MN. Residual A*x-b: 0: 0 1: -4.44089e-16 2: -4.44089e-16 Residual A*x-b: 0: 2.66454e-15 1: 9.99201e-16 2: 8.88178e-16 3: -4.44089e-16 4: 4.44089e-16 Residual A*x-b: 0: -1.11022e-16 1: 0 2: 0 3: 0 4: -1.11022e-16 r8ge_sl_test(): r8ge_sl() solves a linear system A*x=b that was factored by r8ge_fa(). Matrix order N = 10 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 Solution of transposed system: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 r8ge_sl_it_test(): r8ge_sl_it applies one step of iterative refinement to a r8ge_sl solution. Matrix order N = 6 i, x, b-A*x 0: 0.166667 1.13687e-13 1: 0.142857 -9.09495e-13 2: 0.125 1.45519e-11 3: 0.111111 -5.82077e-11 4: 0.1 0 5: 0.0909091 -1.45519e-11 Iterative refinement step 1 I, DX: 0 -1.24677e-11 1 -1.03287e-11 2 -8.79936e-12 3 -7.66042e-12 4 -6.78115e-12 5 -6.08241e-12 i, x, b-A*x 0: 0.166667 -5.68434e-14 1: 0.142857 1.81899e-12 2: 0.125 -2.91038e-11 3: 0.111111 2.91038e-11 4: 0.1 0 5: 0.0909091 7.27596e-12 Iterative refinement step 2 I, DX: 0 -3.60008e-13 1 1.62139e-13 2 3.75167e-13 3 4.65078e-13 4 4.99681e-13 5 5.07613e-13 i, x, b-A*x 0: 0.166667 -1.7053e-13 1: 0.142857 9.09495e-13 2: 0.125 -1.45519e-11 3: 0.111111 8.73115e-11 4: 0.1 -2.91038e-11 5: 0.0909091 3.63798e-11 Iterative refinement step 3 I, DX: 0 1.7504e-11 1 1.43887e-11 2 1.22018e-11 3 1.05912e-11 4 9.35679e-12 5 8.38066e-12 i, x, b-A*x 0: 0.166667 0 1: 0.142857 0 2: 0.125 -2.18279e-11 3: 0.111111 0 4: 0.1 0 5: 0.0909091 -1.45519e-11 Iterative refinement step 4 I, DX: 0 -9.70128e-12 1 -7.53581e-12 2 -6.18456e-12 3 -5.25486e-12 4 -4.57346e-12 5 -4.05139e-12 i, x, b-A*x 0: 0.166667 0 1: 0.142857 1.81899e-12 2: 0.125 2.91038e-11 3: 0.111111 0 4: 0.1 -8.73115e-11 5: 0.0909091 0 Iterative refinement step 5 I, DX: 0 -6.85153e-12 1 -6.66963e-12 2 -6.19756e-12 3 -5.6995e-12 4 -5.24042e-12 5 -4.83331e-12 i, x, b-A*x 0: 0.166667 0 1: 0.142857 0 2: 0.125 0 3: 0.111111 0 4: 0.1 5.82077e-11 5: 0.0909091 7.27596e-12 r8ge_to_r8po_test(): r8ge_to_r8po() converts an R8GE matrix to R8PO format. Matrix order N = 5 The random R8GE matrix: [[0.33806423 0.13463739 0.56343924 0.70042482 0.95061662] [0.33850174 0.88589041 0.94949997 0.79505046 0.68178942] [0.86851963 0.14542995 0.30158333 0.30913017 0.01859047] [0.47218632 0.57106385 0.24892701 0.28236319 0.38193973] [0.51540045 0.83764577 0.99107719 0.3392916 0.44576367]] The R8PO matrix: [[0.33806423 0.13463739 0.56343924 0.70042482 0.95061662] [0. 0.88589041 0.94949997 0.79505046 0.68178942] [0. 0. 0.30158333 0.30913017 0.01859047] [0. 0. 0. 0.28236319 0.38193973] [0. 0. 0. 0. 0.44576367]] r8ge_to_r8pp_test(): r8ge_to_r8pp() converts an R8GE matrix to R8PP format. Matrix order N = 5 The positive definite symmetric R8GE matrix: [[-1. -1. -1. -1. -1.] [-1. 1. 1. 1. 1.] [-1. 1. 3. 3. 3.] [-1. 1. 3. 5. 5.] [-1. 1. 3. 5. 7.]] The RPP matrix: [-1. -1. 1. -1. 1. 3. -1. 1. 3. 5. -1. 1. 3. 5. 7.] r8ge_to_r8vec_test(): r8ge_to_r8vec() converts an R8GE matrix to an R8VEC vector. R8GE matrix: Col: 0 1 2 Row 0 : 11 12 13 1 : 21 22 23 2 : 31 32 33 3 : 41 42 43 Corresponding R8VEC vector: 0: 11 1: 21 2: 31 3: 41 4: 12 5: 22 6: 32 7: 42 8: 13 9: 23 10: 33 11: 43 r8ge_transpose_test(): r8ge_transpose() makes a transposed copy of an R8GE matrix. Indicator matrix A: Col: 0 1 2 3 Row 0 : 11 12 13 14 1 : 21 22 23 24 2 : 31 32 33 34 3 : 41 42 43 44 4 : 51 52 53 54 B = A': Col: 0 1 2 3 4 Row 0 : 11 21 31 41 51 1 : 12 22 32 42 52 2 : 13 23 33 43 53 3 : 14 24 34 44 54 r8ge_transpose_print_test(): r8ge_transpose_print prints the transpose of an R8GE matrix. Here is an R8GE matrix, transposed: Row: 0 1 2 3 Col 0 : 11 21 31 41 1 : 12 22 32 42 2 : 13 23 33 43 r8ge_transpose_print_some_test(): r8ge_transpose_print_some() prints some of an R8GE matrix, transposed. R8GE matrix, rows 0:2, cols 3:5: Row: 0 1 2 Col 3 : 14 24 34 4 : 15 25 35 5 : 16 26 36 r8ge_trf_test(): r8ge_trf() computes the LU factors of an R8GE matrix, so that r8ge_trs() can solve the factored system. Number of matrix rows M = 5 Number of matrix columns N = 5 DEBUG [[0.] [0.] [0.] [0.] [5.]] Solution: 0: 0 1: 0 2: 0 3: 0 4: 5 Solution to transposed system: 0: 1 1: 2 2: 3 3: 4 4: 5 r8ge_trs_test(): r8ge_trs solves a linear system that has been factored by r8ge_trf. Number of matrix rows M = 5 Number of matrix columns N = 5 Solution: 0: 0 1: 0 2: 0 3: 0 4: 5 Solution to transposed system: 0: 1 1: 2 2: 3 3: 4 4: 5 r8ge_zeros_test(): r8ge_zeros zeros out space for a general matrix. Matrix order M, N = 5, 4 Matrix A: Col: 0 1 2 3 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : 0 0 0 0 3 : 0 0 0 0 4 : 0 0 0 0 r8vec_house_column_test(): r8vec_house_column returns the compact form of a Householder matrix that "packs" a column of a matrix. Matrix A: Col: 0 1 2 3 Row 0 : 3.10724 0.231705 1.72698 1.80681 1 : 4.84731 2.2035 2.42122 4.02673 2 : 0.550489 1.39209 0.0712137 4.84506 3 : 3.91286 0.430204 0.580333 4.63634 Working on column K = 0 Householder matrix H: Col: 0 1 2 3 Row 0 : -0.444961 -0.69414 -0.0788306 -0.560326 1 : -0.69414 0.666545 -0.0378692 -0.269173 2 : -0.0788306 -0.0378692 0.995699 -0.0305689 3 : -0.560326 -0.269173 -0.0305689 0.782717 Product H*A: Col: 0 1 2 3 Row 0 : -6.98318 -1.98343 -2.77989 -6.57888 1 :-4.44089e-16 1.13938 0.256179 -0.00164061 2 :-1.38778e-17 1.27124 -0.174661 4.38757 3 :-8.88178e-16 -0.42878 -1.16734 1.38454 Working on column K = 1 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 -0.647324 -0.722238 0.243606 2 : 0 -0.722238 0.683348 0.106804 3 : 0 0.243606 0.106804 0.963976 Product H*A: Col: 0 1 2 3 Row 0 : -6.98318 -1.98343 -2.77989 -6.57888 1 : 8.11271e-17 -1.76014 -0.324055 -2.83053 2 : 2.16393e-16 7.63278e-17 -0.429054 3.1473 3 :-9.65847e-16 -5.55112e-17 -1.08154 1.80287 Working on column K = 2 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 -0.368752 -0.929528 3 : 0 0 -0.929528 0.368752 Product H*A: Col: 0 1 2 3 Row 0 : -6.98318 -1.98343 -2.77989 -6.57888 1 : 8.11271e-17 -1.76014 -0.324055 -2.83053 2 : 8.17987e-16 2.34532e-17 1.16353 -2.83639 3 :-5.57301e-16 -9.14187e-17 1.11022e-16 -2.26069 r8vec_indicator1_test(): r8vec_indicator1 returns the 1-based indicator matrix. The 1-based indicator vector: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 r8vec_to_r8ge_test(): r8vec_to_r8ge converts an R8VEC vector to an R8GE matrix. The R8VEC vector: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 10: 11 11: 12 Corresponding R8GE matrix: Col: 0 1 2 Row 0 : 1 5 9 1 : 2 6 10 2 : 3 7 11 3 : 4 8 12 r8vec2_print_some_test(): r8vec2_print_some prints some of a pair of R8VEC's. Square and square root: 0: 1 1 1: 4 1.41421 2: 9 1.73205 3: 16 2 4: 25 2.23607 5: 36 2.44949 6: 49 2.64575 7: 64 2.82843 ...... .............. .............. 99: 10000 10 r8ge_test(): Normal end of execution. Tue May 20 22:27:34 2025