Tue Sep 27 19:53:31 2022 web_matrix_test(): Python version: 3.6.9 Test web_matrix() Process the "tiny" web matrix power_rank(): Given an NxN incidence matrix A, compute the transition matrix T, Then start with a vector of N values 1/N, and repeatedly compute x <= T*x After many steps, compare last three iterates. If they are close, we are probably at an eigenvector associated with the eigenvalue 1. x, T*x, T*T*x [[1.00000000e+00 1.00000000e+00 1.00000000e+00] [3.25676628e-14 2.42996774e-14 1.81306938e-14] [5.43920813e-14 4.05835087e-14 3.02805324e-14] [7.28990321e-14 5.43920813e-14 4.05835087e-14] [0.00000000e+00 0.00000000e+00 0.00000000e+00]] Process the "moler" web matrix power_rank(): Given an NxN incidence matrix A, compute the transition matrix T, Then start with a vector of N values 1/N, and repeatedly compute x <= T*x After many steps, compare last three iterates. If they are close, we are probably at an eigenvector associated with the eigenvalue 1. x, T*x, T*T*x [[0.01096194 0.01060736 0.01026425] [0.00566419 0.00548097 0.00530368] [0.00292677 0.0028321 0.00274049] [0.00393497 0.00380768 0.00368452] [0.96983974 0.97081533 0.97175936] [0.00667239 0.00645656 0.00624771]] Process the "sauer" web matrix power_rank(): Given an NxN incidence matrix A, compute the transition matrix T, Then start with a vector of N values 1/N, and repeatedly compute x <= T*x After many steps, compare last three iterates. If they are close, we are probably at an eigenvector associated with the eigenvalue 1. x, T*x, T*T*x [[0.01544402 0.01544402 0.01544402] [0.01158301 0.01158301 0.01158301] [0.01158301 0.01158301 0.01158301] [0.01544402 0.01544402 0.01544402] [0.03088803 0.03088803 0.03088803] [0.03088803 0.03088803 0.03088803] [0.03088803 0.03088803 0.03088803] [0.03088803 0.03088803 0.03088803] [0.08108108 0.08108108 0.08108108] [0.11003861 0.11003861 0.11003861] [0.11003861 0.11003861 0.11003861] [0.08108108 0.08108108 0.08108108] [0.14671815 0.14671815 0.14671815] [0.14671815 0.14671815 0.14671815] [0.14671815 0.14671815 0.14671815]] web_matrix_test(): Normal end of execution. Tue Sep 27 19:53:31 2022