Tue May 20 21:19:20 2025 cg_test(): python version: 3.10.12 numpy version: 1.26.4 Test cg(). orth_random_test() orth_random() computes a random orthogal 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 spd_random_test(): 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 r8mat_house_axh_test() r8mat_house_axh() multiplies a matrix A times a compact Householder matrix. Matrix A: Col: 0 1 2 3 4 Row 0 : -3.04809 -0.126345 3.57462 0.0930027 1.67851 1 : -1.84688 3.31694 4.79249 -1.96943 0.57226 2 : -1.53758 0.546444 0.404047 -4.8502 3.31287 3 : -0.796859 -2.43596 4.34087 -0.0580747 -0.236779 4 : 2.96096 -3.24964 3.43824 4.70965 -0.711417 Compact vector V so column 3 of H*A is packed: 0: 0 1: 0 2: 0.732384 3: 0.533748 4: 0.422762 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 -0.0727712 -0.781816 -0.619248 3 : 0 0 -0.781816 0.430226 -0.451296 4 : 0 0 -0.619248 -0.451296 0.642545 Indirect product A*H: Col: 0 1 2 3 4 Row 0 : -3.04809 -0.126345 -1.37225 -3.51219 -1.17703 1 : -1.84688 3.31694 0.836608 -4.85241 -1.71124 2 : -1.53758 0.546444 1.71108 -3.89766 4.06734 3 : -0.796859 -2.43596 -0.123862 -3.31189 -2.81401 4 : 2.96096 -3.24964 -3.49174 -0.340797 -4.71169 Direct product A*H: Col: 0 1 2 3 4 Row 0 : -3.04809 -0.126345 -1.37225 -3.51219 -1.17703 1 : -1.84688 3.31694 0.836608 -4.85241 -1.71124 2 : -1.53758 0.546444 1.71108 -3.89766 4.06734 3 : -0.796859 -2.43596 -0.123862 -3.31189 -2.81401 4 : 2.96096 -3.24964 -3.49174 -0.340797 -4.71169 H*A should pack column 3: Col: 0 1 2 3 4 Row 0 : -3.04809 -0.126345 3.57462 0.0930027 1.67851 1 : -1.84688 3.31694 4.79249 -1.96943 0.57226 2 : -1.09868 3.87704 -5.55229 -2.51808 0.384579 3 : -0.476995 -0.00868214 -4.44089e-16 1.64153 -2.37086 4 : 3.21431 -1.32708 0 6.05585 -2.40175 r8mat_house_form_test(): Python version: 3.10.12 r8mat_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 r8mat_mm_test(): Python version: 3.10.12 r8mat_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 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 : 0.201148 1.00834 4.20922 1.60061 1 : 0.209528 2.21229 0.754185 3.67495 2 : 1.16512 3.83442 1.38211 3.04528 3 : 3.62448 2.64419 3.13044 0.690196 Working on column K = 0 Householder matrix H: Col: 0 1 2 3 Row 0 : -0.0526812 -0.0548761 -0.305147 -0.949262 1 : -0.0548761 0.997139 -0.0159073 -0.0494849 2 : -0.305147 -0.0159073 0.911545 -0.275169 3 : -0.949262 -0.0494849 -0.275169 0.143997 Product H*A: Col: 0 1 2 3 Row 0 : -3.81821 -3.85461 -3.65649 -1.87043 1 :-2.77556e-17 1.95879 0.344147 3.494 2 : 0 2.42477 -0.897969 2.03911 3 :-1.11022e-16 -1.74101 -3.96251 -2.43983 Working on column K = 1 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 -0.548624 -0.679138 0.48763 2 : 0 -0.679138 0.702169 0.213847 3 : 0 0.48763 0.213847 0.846455 Product H*A: Col: 0 1 2 3 Row 0 : -3.81821 -3.85461 -3.65649 -1.87043 1 :-3.89104e-17 -3.57036 -1.5112 -4.49147 2 :-4.89188e-18 3.33067e-16 -1.71162 -1.46286 3 : -1.0751e-16 -2.22045e-16 -3.3783 0.0746286 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 -0.451954 -0.892041 3 : 0 0 -0.892041 0.451954 Product H*A: Col: 0 1 2 3 Row 0 : -3.81821 -3.85461 -3.65649 -1.87043 1 :-3.89104e-17 -3.57036 -1.5112 -4.49147 2 : 9.81142e-17 4.75422e-17 3.78716 0.594574 3 :-4.42257e-17 -3.97463e-16 -2.22045e-16 1.33866 r83_cg_test(): r83_cg() applies CG to an R83 matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 1.07466e-14 Norm of error ||x1-x2|| = 2.75819e-15 r83s_cg_test(): r83s_cg() applies CG to an R83S matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 1.35548e-15 Norm of error ||x1-x2|| = 1.21486e-15 r83t_cg_test(): r83t_cg() applies CG to an R83T matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 1.73866e-15 Norm of error ||x1-x2|| = 8.68887e-16 r8ge_cg_test(): r8ge_cg() applies CG to an R8GE matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 2.59566e-16 Norm of error ||x1-x2|| = 1.21716e-15 r8pbu_cg_test(): r8pbu_cg() applies CG to an R8PBU matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 3.36564e-15 Norm of error ||x1-x2|| = 1.32113e-15 r8sd_cg_test(): r8sd_cg() applies CG to an R8SD matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 7.71186e-16 Norm of error ||x1-x2|| = 4.6444e-16 cg_test(): Normal end of execution. Tue May 20 21:19:20 2025