Fri Aug 12 23:59:25 2022 r8ge_test Python version: 3.6.9 Test r8ge(). i4_log_10_test Python version: 3.6.9 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 Python version: 3.6.9 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|| = 3.66744e-16 Norm of error ||x1-x2|| = 3.81861e-15 r8ge_co_test Python version: 3.6.9 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 Python version: 3.6.9 r8ge_det computes the determinant of an R8GE matrix. r8ge_det computes the determinant = 112 Exact determinant = 112 r8ge_dif2_test Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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 : 0.965717 0.953127 0.564809 0.411787 0.643371 1 : 0.211463 0.741199 0.399248 0.852898 0.165694 2 : 0.0485188 0.960416 0.849691 0.329799 0.362096 3 : 0.571306 0.399714 0.884881 0.932222 0.956106 4 : 0.0322117 0.636241 0.407786 0.167298 0.498778 The compressed LU factors: Col: 0 1 2 3 4 Row 0 : 0.965717 0.953127 0.564809 0.411787 0.643371 1 : -0.21897 0.91253 0.821315 0.30911 0.329773 2 : -0.0502412 -0.583535 0.698484 0.744216 0.634815 3 : -0.591587 0.179878 0.291623 0.799383 0.017508 4 : -0.0333552 -0.662388 0.222027 -0.14267 0.397329 The pivot vector P: 0 0 1 2 2 3 3 3 4 4 Solution: 0: 1 1: 2 2: 3 3: 4 4: 5 r8ge_fs_test Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 r8ge_house_axh multiplies a matrix A times a compact Householder matrix. Matrix A: Col: 0 1 2 3 4 Row 0 : 0.343281 2.80878 3.5612 0.86138 -3.49801 1 : -3.39862 4.77576 -2.96749 -0.802756 1.85862 2 : 3.01257 0.368083 2.81184 -3.96793 2.95409 3 : 2.83373 -1.28526 -0.0906683 1.02983 -4.81051 4 : 4.66951 1.30894 2.78924 4.04447 -0.118057 Compact vector V so column 3 of H*A is packed: 0: 0 1: 0 2: 0.924599 3: -0.0123765 4: 0.38074 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 -0.709768 0.0228866 -0.704064 3 : 0 0 0.0228866 0.999694 0.00942444 4 : 0 0 -0.704064 0.00942444 0.710074 Indirect product A*H: Col: 0 1 2 3 4 Row 0 : 0.343281 2.80878 -0.0450846 0.909653 -4.98304 1 : -3.39862 4.77576 0.779274 -0.852909 3.4015 2 : 3.01257 0.368083 -4.16643 -3.87452 0.0805104 3 : 2.83373 -1.28526 3.47483 0.982102 -3.34228 4 : 4.66951 1.30894 -1.80403 4.10596 -2.00952 Direct product A*H: Col: 0 1 2 3 4 Row 0 : 0.343281 2.80878 -0.0450846 0.909653 -4.98304 1 : -3.39862 4.77576 0.779274 -0.852909 3.4015 2 : 3.01257 0.368083 -4.16643 -3.87452 0.0805104 3 : 2.83373 -1.28526 3.47483 0.982102 -3.34228 4 : 4.66951 1.30894 -1.80403 4.10596 -2.00952 H*A should pack column 3: Col: 0 1 2 3 4 Row 0 : 0.343281 2.80878 3.5612 0.86138 -3.49801 1 : -3.39862 4.77576 -2.96749 -0.802756 1.85862 2 : -5.361 -1.21225 -3.96164 -0.00768837 -2.12369 3 : 2.94581 -1.26411 -3.46945e-18 0.976818 -4.74254 4 : 1.22137 0.65818 0 5.67526 -2.20903 r8ge_house_form_test Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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: 25.6697 25.6697 1: 20.0519 20.0519 2: 31.7259 31.7259 3: 25.8187 25.8187 4: 25.0653 25.0653 5: 27.9361 27.9361 6: 10.109 10.109 7: 27.5894 27.5894 8: 18.5708 18.5708 9: 34.4201 34.4201 A'*x and (PLU)'*x 0: 31.817 31.817 1: 28.2626 28.2626 2: 24.7737 24.7737 3: 32.7707 32.7707 4: 25.305 25.305 5: 27.833 27.833 6: 19.2309 19.2309 7: 24.3941 24.3941 8: 20.1988 20.1988 9: 32.3563 32.3563 r8ge_mm_test Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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: 3.09417 3.09417 1: 3.82291 3.82291 2: 4.40491 4.40491 3: 4.38181 4.38181 4: 3.97778 3.97778 A'*x and (PLU)'*x 0: 3.4187 3.4187 1: 4.98489 4.98489 2: 10.7645 10.7645 Matrix is 3 by 5 A*x and PLU*x 0: 8.18563 8.18563 1: 5.16106 5.16106 2: 8.82864 8.82864 A'*x and (PLU)'*x 0: 5.23203 5.23203 1: 4.44139 4.44139 2: 2.51711 2.51711 3: 2.86509 2.86509 4: 1.66186 1.66186 r8ge_mv_test Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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 : 0.511546 0.597281 0.739694 0.0947821 1 : 0.21844 0.0605904 0.74953 0.760736 2 : 0.15801 0.207352 0.0432688 0.512537 3 : 0.870322 0.545064 0.0689965 0.264023 4 : 0.986369 0.861822 0.850338 0.766743 Factor P: Col: 0 1 2 3 4 Row 0 : 0 0 0 0 1 1 : 0 0 1 0 0 2 : 0 0 0 1 0 3 : 0 1 0 0 0 4 : 1 0 0 0 0 Factor L: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : 0.882349 1 0 0 0 2 : 0.221458 0.604872 1 0 0 3 : 0.160193 -0.321754 -0.320719 1 0 4 : 0.518615 -0.698018 -0.181711 -0.83202 1 Factor U: Col: 0 1 2 3 Row 0 : 0.986369 0.861822 0.850338 0.766743 1 : 0 -0.215363 -0.681298 -0.412512 2 : 0 0 0.973314 0.840451 3 : 0 0 0 0.526531 4 : 0 0 0 0 Product P*L*U: Col: 0 1 2 3 Row 0 : 0.511546 0.597281 0.739694 0.0947821 1 : 0.21844 0.0605904 0.74953 0.760736 2 : 0.15801 0.207352 0.0432688 0.512537 3 : 0.870322 0.545064 0.0689965 0.264023 4 : 0.986369 0.861822 0.850338 0.766743 r8ge_poly_test Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 r8ge_random computes a random R8GE. 0 <= X <= 1 Random R8GE: Col: 0 1 2 3 Row 0 : 0.649973 0.946487 0.173419 0.177892 1 : 0.518456 0.769474 0.525587 0.649684 2 : 0.592511 0.544677 0.973882 0.666595 3 : 0.0320278 0.83084 0.169389 0.603694 4 : 0.395468 0.339122 0.586397 0.424103 r8ge_random_ab_test Python version: 3.6.9 r8ge_random_ab computes a random R8GE. -1 <= X <= 5 Random R8GE: Col: 0 1 2 3 Row 0 : -0.372512 3.27986 -0.662025 4.88285 1 : 2.54262 -0.784434 1.84283 4.64843 2 : 0.355369 4.65893 -0.935691 1.75525 3 : 2.98491 -0.738417 1.8244 2.21765 4 : -0.280533 2.33962 -0.75413 1.69599 r8ge_res_test Python version: 3.6.9 r8ge_res computes b-A*x, where A is an R8GE matrix. We check three cases, MN. Residual A*x-b: 0: 7.77156e-16 1: -8.88178e-16 2: -1.77636e-15 Residual A*x-b: 0: 0 1: 2.22045e-16 2: 0 3: 4.44089e-16 4: -7.77156e-16 Residual A*x-b: 0: 2.22045e-16 1: -2.22045e-16 2: 2.22045e-16 3: 0 4: 0 r8ge_sl_test Python version: 3.6.9 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 Python version: 3.6.9 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: [[0.75280664 0.84117284 0.85783235 0.5017785 0.38216845] [0.86429363 0.67194208 0.20395784 0.29767483 0.99533163] [0.14458216 0.50512679 0.98962745 0.41581275 0.27377342] [0.0364585 0.07301604 0.39129413 0.11813922 0.719169 ] [0.55529257 0.14423404 0.78626443 0.44092885 0.34258329]] The R8PO matrix: [[0.75280664 0.84117284 0.85783235 0.5017785 0.38216845] [0. 0.67194208 0.20395784 0.29767483 0.99533163] [0. 0. 0.98962745 0.41581275 0.27377342] [0. 0. 0. 0.11813922 0.719169 ] [0. 0. 0. 0. 0.34258329]] 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 Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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 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 Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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 : 2.09836 1.63199 0.481879 1.55821 1 : 3.93088 0.558191 1.88754 0.576407 2 : 0.520219 1.99213 0.9968 2.88266 3 : 0.785995 3.61776 3.93763 3.13554 Working on column K = 0 Householder matrix H: Col: 0 1 2 3 Row 0 : -0.460723 -0.863079 -0.114221 -0.172576 1 : -0.863079 0.490043 -0.0674884 -0.101968 2 : -0.114221 -0.0674884 0.991068 -0.0134946 3 : -0.172576 -0.101968 -0.0134946 0.979611 Product H*A: Col: 0 1 2 3 Row 0 : -4.55449 -2.08554 -2.64451 -2.08577 1 : 7.21645e-16 -1.63834 0.0402954 -1.57667 2 : 1.56125e-16 1.70143 0.752333 2.59772 3 : 0 3.17856 3.56826 2.70503 Working on column K = 1 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 -0.413713 0.429646 0.802649 2 : 0 0.429646 0.869425 -0.243936 3 : 0 0.802649 -0.243936 0.544288 Product H*A: Col: 0 1 2 3 Row 0 : -4.55449 -2.08554 -2.64451 -2.08577 1 : -2.31475e-16 3.96008 3.17063 3.93958 2 : 4.45791e-16 1.11022e-16 -0.199017 0.921263 3 : 5.41143e-16 -2.22045e-16 1.79098 -0.426874 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 -0.110442 0.993883 3 : 0 0 0.993883 0.110442 Product H*A: Col: 0 1 2 3 Row 0 : -4.55449 -2.08554 -2.64451 -2.08577 1 : -2.31475e-16 3.96008 3.17063 3.93958 2 : 4.88599e-16 -2.32948e-16 1.80201 -0.526008 3 : 5.02829e-16 8.58201e-17 1.11022e-16 0.868482 r8vec_indicator1_test Python version: 3.6.9 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 Python version: 3.6.9 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 Python version: 3.6.9 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. Fri Aug 12 23:59:25 2022