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