Wed Oct 8 08:50:31 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|| = 3.23325e-16 Norm of error ||x1-x2|| = 1.72872e-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 : 0.48196 0.0386226 0.21828 0.44571 0.745868 1 : 0.0540596 0.755643 0.329563 0.35395 0.353521 2 : 0.774454 0.534136 0.606059 0.237413 0.900231 3 : 0.506718 0.801022 0.878198 0.849222 0.82819 4 : 0.201254 0.14164 0.835506 0.702685 0.788326 The compressed LU factors: Col: 0 1 2 3 4 Row 0 : 0.774454 0.534136 0.606059 0.237413 0.900231 1 : -0.0698035 0.718358 0.287258 0.337378 0.290681 2 : -0.622323 0.408964 0.676878 0.639657 0.553239 3 : -0.65429 -0.628575 -0.444831 0.475067 0.338355 4 : -0.259866 -0.00394895 0.0611725 -0.415263 -0.330142 The pivot vector P: 0 2 1 1 2 4 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 : 0.707329 -1.93852 3.59934 -1.3271 -3.71119 1 : 3.88705 2.29612 -0.437361 3.34627 0.433327 2 : 1.37903 -1.50472 2.13173 3.42319 -4.75207 3 : 3.57847 1.69021 4.5815 4.6791 1.41698 4 : 2.70277 2.87711 4.95712 -0.892685 2.26384 Compact vector V so column 3 of H*A is packed: 0: 0 1: 0 2: 0.806582 3: 0.401216 4: 0.43411 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 -0.301149 -0.647227 -0.70029 3 : 0 0 -0.647227 0.678052 -0.348344 4 : 0 0 -0.70029 -0.348344 0.623097 Indirect product A*H: Col: 0 1 2 3 4 Row 0 : 0.707329 -1.93852 2.3739 -1.93666 -4.37073 1 : 3.88705 2.29612 -2.33754 2.40107 -0.589368 2 : 1.37903 -1.50472 0.470282 2.59674 -5.64628 3 : 3.57847 1.69021 -5.40045 -0.286199 -3.9554 4 : 2.70277 2.87711 -2.50041 -4.60226 -1.74987 Direct product A*H: Col: 0 1 2 3 4 Row 0 : 0.707329 -1.93852 2.3739 -1.93666 -4.37073 1 : 3.88705 2.29612 -2.33754 2.40107 -0.589368 2 : 1.37903 -1.50472 0.470282 2.59674 -5.64628 3 : 3.57847 1.69021 -5.40045 -0.286199 -3.9554 4 : 2.70277 2.87711 -2.50041 -4.60226 -1.74987 H*A should pack column 3: Col: 0 1 2 3 4 Row 0 : 0.707329 -1.93852 3.59934 -1.3271 -3.71119 1 : 3.88705 2.29612 -0.437361 3.34627 0.433327 2 : -4.6241 -2.65562 -7.07867 -3.43419 -1.07137 3 : 0.592353 1.11772 0 1.26805 3.24786 4 : -0.528168 2.25768 -8.88178e-16 -4.58339 4.24483 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: 34.4386 34.4386 1: 24.9708 24.9708 2: 22.051 22.051 3: 27.1694 27.1694 4: 27.1977 27.1977 5: 21.4574 21.4574 6: 26.5101 26.5101 7: 23.2351 23.2351 8: 24.3585 24.3585 9: 31.8274 31.8274 A'*x and (PLU)'*x 0: 31.1644 31.1644 1: 23.9803 23.9803 2: 16.74 16.74 3: 33.7657 33.7657 4: 21.4135 21.4135 5: 31.2163 31.2163 6: 21.2143 21.2143 7: 34.2277 34.2277 8: 22.667 22.667 9: 14.9899 14.9899 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: 1.98823 1.98823 1: 4.3215 4.3215 2: 3.07439 3.07439 3: 2.22562 2.22562 4: 1.71812 1.71812 A'*x and (PLU)'*x 0: 9.89962 9.89962 1: 7.19172 7.19172 2: 7.75427 7.75427 Matrix is 3 by 5 A*x and PLU*x 0: 2.58854 2.58854 1: 12.4448 12.4448 2: 7.4931 7.4931 A'*x and (PLU)'*x 0: 3.65446 3.65446 1: 2.69942 2.69942 2: 1.67488 1.67488 3: 2.24221 2.24221 4: 2.3185 2.3185 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 : 0.377812 0.492124 0.157259 0.385379 1 : 0.156031 0.755822 0.107096 0.0311194 2 : 0.793532 0.344111 0.716726 0.853029 3 : 0.929014 0.225389 0.12124 0.531435 4 : 0.759205 0.0492181 0.754255 0.731656 Factor P: Col: 0 1 2 3 4 Row 0 : 0 0 0 1 0 1 : 0 1 0 0 0 2 : 0 0 0 0 1 3 : 1 0 0 0 0 4 : 0 0 1 0 0 Factor L: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : 0.167953 1 0 0 0 2 : 0.817216 -0.187993 1 0 0 3 : 0.406681 0.557773 0.0887216 1 0 4 : 0.854166 0.211139 0.885883 0.894238 1 Factor U: Col: 0 1 2 3 Row 0 : 0.929014 0.225389 0.12124 0.531435 1 : 0 0.717968 0.0867338 -0.0581365 2 : 0 0 0.671481 0.28643 3 : 0 0 0 0.176269 4 : 0 0 0 0 Product P*L*U: Col: 0 1 2 3 Row 0 : 0.377812 0.492124 0.157259 0.385379 1 : 0.156031 0.755822 0.107096 0.0311194 2 : 0.793532 0.344111 0.716726 0.853029 3 : 0.929014 0.225389 0.12124 0.531435 4 : 0.759205 0.0492181 0.754255 0.731656 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 : 0.118727 0.994509 0.146473 0.389994 1 : 0.320206 0.206506 0.308235 0.983836 2 : 0.108057 0.702112 0.664339 0.809753 3 : 0.227405 0.495359 0.732783 0.122508 4 : 0.609515 0.498049 0.666922 0.0184229 r8ge_random_ab_test(): r8ge_random_ab computes a random R8GE. -1 <= X <= 5 Random R8GE: Col: 0 1 2 3 Row 0 : 3.35357 3.58639 4.24231 2.25138 1 : 3.93693 3.71472 -0.405104 1.79725 2 : 2.59081 3.63949 3.28034 -0.73886 3 : -0.853086 1.12131 1.87505 3.75564 4 : 0.706366 4.46735 1.96705 2.79533 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: -6.66134e-16 1: -8.88178e-16 2: -4.44089e-16 Residual A*x-b: 0: 0 1: 0 2: -8.88178e-16 3: 0 4: -4.44089e-16 Residual A*x-b: 0: 0 1: 2.22045e-16 2: 0 3: 2.22045e-16 4: 0 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: [[0.996823 0.35126793 0.76046322 0.98688728 0.52977356] [0.01359874 0.81801248 0.22995586 0.16125875 0.59251996] [0.13403054 0.38806445 0.56377802 0.25878972 0.32265028] [0.92938737 0.39950804 0.48654964 0.01494505 0.18278508] [0.08340051 0.07096505 0.55132179 0.58300986 0.96573852]] The R8PO matrix: [[0.996823 0.35126793 0.76046322 0.98688728 0.52977356] [0. 0.81801248 0.22995586 0.16125875 0.59251996] [0. 0. 0.56377802 0.25878972 0.32265028] [0. 0. 0. 0.01494505 0.18278508] [0. 0. 0. 0. 0.96573852]] 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 : 1.45506 0.210563 0.208896 3.60149 1 : 1.35373 2.03334 4.81475 0.530881 2 : 2.74311 2.1117 1.98015 2.09394 3 : 4.59905 3.95827 0.386047 3.60399 Working on column K = 0 Householder matrix H: Col: 0 1 2 3 Row 0 : -0.254742 -0.237002 -0.480246 -0.805171 1 : -0.237002 0.955234 -0.0907112 -0.152085 2 : -0.480246 -0.0907112 0.816188 -0.308175 3 : -0.805171 -0.152085 -0.308175 0.48332 Product H*A: Col: 0 1 2 3 Row 0 : -5.71189 -4.73676 -2.45611 -4.9507 1 : 1.11022e-16 1.09887 4.31137 -1.0845 2 : 0 0.218133 0.960135 -1.17937 3 : 0 0.783559 -1.3241 -1.88397 Working on column K = 1 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 -0.803775 -0.159555 -0.573139 2 : 0 -0.159555 0.985886 -0.0506976 3 : 0 -0.573139 -0.0506976 0.817888 Product H*A: Col: 0 1 2 3 Row 0 : -5.71189 -4.73676 -2.45611 -4.9507 1 :-8.92369e-17 -1.36714 -2.85967 2.13964 2 :-1.77141e-17 2.77556e-17 0.325813 -0.894179 3 :-6.36312e-17 1.11022e-16 -3.60265 -0.859517 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 -0.0900694 0.995935 3 : 0 0 0.995935 0.0900694 Product H*A: Col: 0 1 2 3 Row 0 : -5.71189 -4.73676 -2.45611 -4.9507 1 :-8.92369e-17 -1.36714 -2.85967 2.13964 2 :-6.17771e-17 1.08071e-16 -3.61735 -0.775485 3 :-2.33734e-17 3.76425e-17 3.33067e-16 -0.967961 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. Wed Oct 8 08:50:31 2025