Tue Jun  4 18:28:39 2024

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:
[[12.23467633  1.46714388 -0.1535146   0.09488267 -0.44125675]
 [ 1.46714388 11.8013955  -0.12698773  0.14971928 -0.32729231]
 [-0.1535146  -0.12698773 10.66860546  0.52138698  0.15859667]
 [ 0.09488267  0.14971928  0.52138698 12.90517937  0.30540313]
 [-0.44125675 -0.32729231  0.15859667  0.30540313 10.84390414]]

  Eigenvectors Q:
[[-0.73875706  0.41295336  0.06383692  0.52709898  0.04241517]
 [-0.63684223 -0.47970804  0.02550643 -0.54123263  0.26594895]
 [ 0.05585081 -0.70514827 -0.22436321  0.64252994  0.19095296]
 [-0.11048547  0.1299202  -0.95816093 -0.12507395 -0.19286741]
 [ 0.1826024   0.29195272 -0.1638995  -0.02730726  0.92401907]]

  Eigenvalues lamda:
[10.5103918  10.54140477 10.69847767 13.06920156 13.63428501]

  Computed eigenvectors Q2:
[[ 0.73875706  0.06383692 -0.41295336  0.52709898  0.04241517]
 [ 0.63684223  0.02550643  0.47970804 -0.54123263  0.26594895]
 [-0.05585081 -0.22436321  0.70514827  0.64252994  0.19095296]
 [ 0.11048547 -0.95816093 -0.1299202  -0.12507395 -0.19286741]
 [-0.1826024  -0.1638995  -0.29195272 -0.02730726  0.92401907]]

  Computed eigenvalues lamda2:
[10.5103918  10.54140477 10.69847767 13.06920156 13.63428501]

  Norm of eigenvalue error =  2.5803073537982523e-14

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

  Real nonsymmetric test matrix A:
[[  4.49935688  17.0563023    0.13389198   3.82284583  -8.84364565]
 [-11.41321778  24.07351072  -8.84138075   1.07415807  -9.14153287]
 [ -7.18145024  -0.50445771   4.76174369  -0.07709551  -2.41836647]
 [  2.49616628  18.64711484  -4.99737118   9.07846884  -0.67160853]
 [  1.76047248  -6.55377646   2.13661705  -1.42011171   6.47529736]]

  Orthogonal factor Q:
[[-0.48447055  0.00597837  0.37992186 -0.77282663  0.15378857]
 [-0.6353436  -0.66295412 -0.2773514   0.22198371 -0.17501363]
 [ 0.29090514 -0.38445599 -0.40406705 -0.2366254   0.74047689]
 [ 0.49439772 -0.45397155 -0.0325096  -0.44692699 -0.59049142]
 [ 0.18047685 -0.45448818  0.78384216  0.31261304  0.22075588]]

  Schur upper triangle T:
[[13.08937618 15.44906752 10.54524957  8.52282879 12.41576187]
 [ 0.          6.80314156 17.43302973  6.88577145 15.47153507]
 [ 0.          0.         11.78774677  7.5725993  11.84913393]
 [ 0.          0.          0.          8.6804391   6.60736653]
 [ 0.          0.          0.          0.          8.52767389]]

  Sorted eigenvalues lamda:
[ 6.80314156  8.52767389  8.6804391  11.78774677 13.08937618]

  Computed eigenvectors Q2:
[[ 0.48447055  0.44435313 -0.30514475 -0.29702418 -0.20928656]
 [-0.00597837 -0.06030041  0.18483948  0.19064505  0.25540109]
 [-0.37992186 -0.40652693  0.45179252  0.45266171  0.45643716]
 [ 0.77282663  0.7816077  -0.80166314 -0.80248147 -0.79949992]
 [-0.15378857 -0.15079593  0.16106142  0.16294774  0.20840926]]

  Computed eigenvalues lamda2:
[ 6.80314156  8.52767389  8.6804391  11.78774677 13.08937618]

  Norm of eigenvalue error =  2.225490671845925e-11

eigs_test():
  Normal end of execution.
Tue Jun  4 18:28:39 2024