Tue Oct 19 11:55:07 2021

jacobi_eigenvalue_test():
  Python version: 3.6.9
  Test jacobi_eigenvalue().

jacobi_eigenvalue_test01
  Python version: 3.6.9
  jacobi_eigenvalue computes the eigenvalues D
  and eigenvectors V of a symmetric matrix A so that A * V = D * V.

  Input matrix A:

  Col:       0             1             2             3       
  Row
      0 :           4           -30            60           -35  
      1 :         -30           300          -675           420  
      2 :          60          -675          1620         -1050  
      3 :         -35           420         -1050           700  

  Number of iterations = 11
  Number of rotations  = 21

  Eigenvalues D:

     0:      0.166643
     1:       1.47805
     2:       37.1015
     3:       2585.25

  Eigenvector matrix V:

  Col:       0             1             2             3       
  Row
      0 :    0.792608      0.582076      0.179186     0.0291933  
      1 :    0.451923     -0.370502     -0.741918     -0.328712  
      2 :    0.322416     -0.509579      0.100228      0.791411  
      3 :    0.252161     -0.514048      0.638283     -0.514553  

  Frobenius norm error in eigensystem A*V-D*V = 1.20349e-12

jacobi_eigenvalue_test01
  Normal end of execution.

jacobi_eigenvalue_test02
  Python version: 3.6.9
  jacobi_eigenvalue computes the eigenvalues D
  and eigenvectors V of a symmetric matrix so that A * V = D * V.

  As a sanity check, input a diagonal matrix.

  Input matrix A:

  Col:       0             1             2             3       
  Row
      0 :           4             0             0             0  
      1 :           0             1             0             0  
      2 :           0             0             3             0  
      3 :           0             0             0             2  

  Number of iterations = 1
  Number of rotations  = 0

  Eigenvalues D:

     0:             1
     1:             2
     2:             3
     3:             4

  Eigenvector matrix V:

  Col:       0             1             2             3       
  Row
      0 :           0             0             0             1  
      1 :           1             0             0             0  
      2 :           0             0             1             0  
      3 :           0             1             0             0  

  Frobenius norm error in eigensystem A*V-D*V = 0

jacobi_eigenvalue_test02
  Normal end of execution.

jacobi_eigenvalue_test03
  Python version: 3.6.9
  jacobi_eigenvalue computes the eigenvalues D
  and eigenvectors V of a symmetric matrix so that A * V = D * V.

  Use the discretized second derivative matrix.

  Input matrix A:

  Col:       0             1             2             3             4       
  Row
      0 :          -2             1             0             0             0  
      1 :           1            -2             1             0             0  
      2 :           0             1            -2             1             0  
      3 :           0             0             1            -2             1  
      4 :           0             0             0             1            -2  

  Number of iterations = 10
  Number of rotations  = 43

  Eigenvalues D:

     0:      -3.73205
     1:            -3
     2:            -2
     3:            -1
     4:     -0.267949

  Eigenvector matrix V:

  Col:       0             1             2             3             4       
  Row
      0 :    0.288675           0.5       0.57735          -0.5      0.288675  
      1 :        -0.5          -0.5  -4.44985e-17          -0.5           0.5  
      2 :     0.57735   5.05017e-17      -0.57735   -7.0576e-17       0.57735  
      3 :        -0.5           0.5   1.86451e-16           0.5           0.5  
      4 :    0.288675          -0.5       0.57735           0.5      0.288675  

  Frobenius norm error in eigensystem A*V-D*V = 9.40195e-16

jacobi_eigenvalue_test03
  Normal end of execution.

jacobi_eigenvalue_test():
  Normal end of execution.
Tue Oct 19 11:55:07 2021