Tue May 20 21:35:29 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:
[[ 6.90324396  1.97780789  0.21968301  0.3898811   0.81708095]
 [ 1.97780789  9.47193978  0.84436999  5.4532834   2.03744944]
 [ 0.21968301  0.84436999  7.64662674 -1.0274158   3.40630362]
 [ 0.3898811   5.4532834  -1.0274158   9.1238286  -1.50047541]
 [ 0.81708095  2.03744944  3.40630362 -1.50047541 13.4238331 ]]

  Eigenvectors Q:
[[-0.18634506  0.23716426 -0.07369586 -0.12154089 -0.94277535]
 [-0.47459265 -0.68655769 -0.06059512 -0.54746298 -0.00358962]
 [-0.34388745  0.13588457 -0.89003699  0.22528203  0.14268485]
 [-0.165586    0.65338312  0.03640745 -0.68172312  0.28213446]
 [-0.77094749  0.16437013  0.44430372  0.41232717  0.1058439 ]]

  Eigenvalues lamda:
[ 2.94403768  6.06391347  6.66911842 14.81969281 16.0727098 ]

  Computed eigenvectors Q2:
[[-0.18634506 -0.12154089 -0.23716426  0.94277535 -0.07369586]
 [-0.47459265 -0.54746298  0.68655769  0.00358962 -0.06059512]
 [-0.34388745  0.22528203 -0.13588457 -0.14268485 -0.89003699]
 [-0.165586   -0.68172312 -0.65338312 -0.28213446  0.03640745]
 [-0.77094749  0.41232717 -0.16437013 -0.1058439   0.44430372]]

  Computed eigenvalues lamda2:
[ 2.94403768  6.06391347  6.66911842 14.81969281 16.0727098 ]

  Norm of eigenvalue error =  8.837263695108354e-15

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

  Real nonsymmetric test matrix A:
[[  7.13996342   0.2375756    2.39617738  -6.12422069  -5.13007474]
 [ 19.80687021  17.24580347  -2.79775383 -12.8021568  -12.58714476]
 [  5.24393269  18.19486717  12.04183678  -0.44608801 -13.26014567]
 [ -2.66356901  -1.39550894   0.49357841  11.79044524   1.94453569]
 [ -8.82514234   0.2032994    2.68853963   0.25251019   9.28095031]]

  Orthogonal factor Q:
[[-0.33154609 -0.03590374 -0.8216409   0.0862747  -0.45414868]
 [ 0.54122826 -0.67722185 -0.10445222  0.48357308 -0.06073996]
 [-0.07459519 -0.32765098 -0.41479535 -0.36942799  0.76062354]
 [-0.68197207 -0.61112014  0.37580831 -0.0288751  -0.13921431]
 [-0.35566673  0.24343067 -0.02662519  0.78829115  0.43832732]]

  Schur upper triangle T:
[[ 7.67043514 11.28790531 15.80393033  6.37020432  4.64451954]
 [ 0.          8.39890675  6.22390329 15.42842283 12.39566682]
 [ 0.          0.         18.4031997  14.65076013 10.0147715 ]
 [ 0.          0.          0.         12.27077829 14.9833932 ]
 [ 0.          0.          0.          0.         10.75567934]]

  Sorted eigenvalues lamda:
[ 7.67043514  8.39890675 10.75567934 12.27077829 18.4031997 ]

  Computed eigenvectors Q2:
[[-0.18222757 -0.24665345 -0.29148512  0.29600184  0.33154609]
 [-0.33948535 -0.04392341  0.24578713  0.07944339  0.03590374]
 [-0.91614101 -0.95656312 -0.86819193  0.82666211  0.8216409 ]
 [ 0.04726348 -0.0524449  -0.28140365 -0.11723849 -0.0862747 ]
 [-0.09997313 -0.1395326   0.14724085  0.45711765  0.45414868]]

  Computed eigenvalues lamda2:
[ 7.67043514  8.39890675 10.75567934 12.27077829 18.4031997 ]

  Norm of eigenvalue error =  2.9121012374600575e-13

eigs_test():
  Normal end of execution.
Tue May 20 21:35:29 2025