07-Jan-2022 21:57:45

jacobi_eigenvalue_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Test jacobi_eigenvalue().

jacobi_eigenvalue_test01()
  jacobi_eigenvalue() computes the eigenvalues D
  and eigenvectors V so that A * V = D * V.

  Input matrix A:

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

  Number of iterations = 11
  Number of rotations  = 21

  Eigenvalues D:

     1:     0.166643
     2:      1.47805
     3:      37.1015
     4:      2585.25

  Eigenvector matrix V:

  Col:       1             2             3             4       
  Row
      1 :    0.792608      0.582076      0.179186     0.0291933  
      2 :    0.451923     -0.370502     -0.741918     -0.328712  
      3 :    0.322416     -0.509579      0.100228      0.791411  
      4 :    0.252161     -0.514048      0.638283     -0.514553  

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

jacobi_eigenvalue_test02()
  jacobi_eigenvalue() computes the eigenvalues D
  and eigenvectors V so that A * V = D * V.

  As a "sanity check", input a diagonal matrix.

  Input matrix A:

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

  Number of iterations = 1
  Number of rotations  = 0

  Eigenvalues D:

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

  Eigenvector matrix V:

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

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

jacobi_eigenvalue_test03()
  jacobi_eigenvalue() computes the eigenvalues D
  and eigenvectors V so that A * V = D * V.

  Use the discretized second derivative matrix.

  Input matrix A:

  Col:       1             2             3             4             5       
  Row
      1 :          -2             1             0             0             0  
      2 :           1            -2             1             0             0  
      3 :           0             1            -2             1             0  
      4 :           0             0             1            -2             1  
      5 :           0             0             0             1            -2  

  Number of iterations = 10
  Number of rotations  = 43

  Eigenvalues D:

     1:     -3.73205
     2:           -3
     3:           -2
     4:           -1
     5:    -0.267949

  Eigenvector matrix V:

  Col:       1             2             3             4             5       
  Row
      1 :    0.288675           0.5       0.57735          -0.5      0.288675  
      2 :        -0.5          -0.5  -4.44985e-17          -0.5           0.5  
      3 :     0.57735   5.05017e-17      -0.57735   -7.0576e-17       0.57735  
      4 :        -0.5           0.5   1.86451e-16           0.5           0.5  
      5 :    0.288675          -0.5       0.57735           0.5      0.288675  

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

jacobi_eigenvalue_test():
  Normal end of execution.

07-Jan-2022 21:57:46