Wed Oct  8 07:44:16 2025

eigs_test():
  python version: 3.10.12
  numpy version:  1.26.4
  Test np.linalg.eig(), a built-in function for computing
  eigenvalues and eigenvectors.

eigs_symmetric_test():
  Test eigs() on a real symmetric matrix.

  Real symmetric test matrix A:
[[ 5.4955374   4.15594407 -1.5033547   0.16627993 -0.67076415]
 [ 4.15594407  6.8411443  -0.25297252 -0.24546568  2.18077961]
 [-1.5033547  -0.25297252  9.23503152  0.6366166  -0.57138897]
 [ 0.16627993 -0.24546568  0.6366166  10.15793693 -0.08907037]
 [-0.67076415  2.18077961 -0.57138897 -0.08907037 11.97089423]]

  Eigenvectors Q:
[[-0.37182353 -0.21415723 -0.73514749  0.2755106  -0.44669455]
 [-0.22400157 -0.4419142   0.63594703  0.47150759 -0.35747323]
 [ 0.52096678  0.2487701  -0.13802178  0.7885812   0.1606136 ]
 [ 0.58553347  0.10218153  0.04010812 -0.25705772 -0.76093506]
 [ 0.44420122 -0.82856556 -0.18566335 -0.1176245   0.26049564]]

  Eigenvalues lamda:
[ 1.43966901  8.43624696 10.03635242 10.64509753 13.14317844]

  Computed eigenvectors Q2:
[[ 0.73514749 -0.21415723 -0.2755106  -0.44669455 -0.37182353]
 [-0.63594703 -0.4419142  -0.47150759 -0.35747323 -0.22400157]
 [ 0.13802178  0.2487701  -0.7885812   0.1606136   0.52096678]
 [-0.04010812  0.10218153  0.25705772 -0.76093506  0.58553347]
 [ 0.18566335 -0.82856556  0.1176245   0.26049564  0.44420122]]

  Computed eigenvalues lamda2:
[ 1.43966901  8.43624696 10.03635242 10.64509753 13.14317844]

  Norm of eigenvalue error =  2.6822400070865448e-14

eigs_nonsymmetric_test():
  Test eigs() on a nonsymmetric matrix.

  Real nonsymmetric test matrix A:
[[ 12.08106416   7.81352019  17.66165057  -4.53265593  -1.78289615]
 [ -0.36221949  12.83961183  -1.30672112   1.08465128  -5.43401776]
 [  0.98684782   6.75295742  19.17049303   0.03170275 -16.75428293]
 [ -2.8051345   -0.52356302  -3.74925384  11.86560608   1.19598621]
 [  0.03863059   1.69686214   0.31761368  -0.25721574  10.50678844]]

  Orthogonal factor Q:
[[-0.71314912  0.29020585 -0.10033126  0.62784543  0.05424613]
 [-0.59588349 -0.36335597 -0.38921694 -0.5501498  -0.24236476]
 [ 0.29328091 -0.5524176  -0.52880869  0.52412947 -0.23338974]
 [ 0.15823113  0.38755967 -0.71341361 -0.1599607   0.53871515]
 [-0.15902957 -0.57304913  0.22326264  0.05334965  0.77047511]]

  Schur upper triangle T:
[[15.51233668  7.32069797 12.66171176  9.24801822  2.07946186]
 [ 0.         14.71044129  9.47468601  9.55057632  9.06587618]
 [ 0.          0.          8.87576999  5.67956195 11.06497861]
 [ 0.          0.          0.         17.22074066  7.471233  ]
 [ 0.          0.          0.          0.         10.14427491]]

  Sorted eigenvalues lamda:
[ 8.87576999 10.14427491 14.71044129 15.51233668 17.22074066]

  Computed eigenvectors Q2:
[[ 0.7034717  -0.36517129 -0.644025    0.71314912 -0.79262281]
 [ 0.00197782 -0.06409268  0.328045   -0.29020585  0.2258883 ]
 [ 0.06015027 -0.17719975 -0.05735412  0.10033126 -0.19162435]
 [ 0.70357771 -0.90014394  0.68401642 -0.62784543  0.53242047]
 [ 0.08052337 -0.14451017  0.08031392 -0.05424613  0.02306724]]

  Computed eigenvalues lamda2:
[ 8.87576999 10.14427491 14.71044129 15.51233668 17.22074066]

  Norm of eigenvalue error =  8.539455607861096e-14

eigs_test():
  Normal end of execution.
Wed Oct  8 07:44:16 2025