15 July 2013 09:22:28 PM

JACOBI_EIGENVALUE_TEST
  C++ version
  Test the JACOBI_EIGENVALUE library.

TEST01
  For a symmetric matrix A,
  JACOBI_EIGENVALUE computes the eigenvalues D
  and eigenvectors V 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:        2585.25
         1:        37.1015
         2:        1.47805
         3:       0.166643

  Eigenvector matrix V:

  Col:          0             1             2             3       
  Row

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

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

TEST02
  For a symmetric matrix A,
  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:          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:              4
         1:              3
         2:              2
         3:              1

  Eigenvector matrix V:

  Col:          0             1             2             3       
  Row

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

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

TEST03
  For a symmetric matrix A,
  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:          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:      -0.267949
         1:             -1
         2:             -2
         3:             -3
         4:       -3.73205

  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   -7.0576e-17      -0.57735   5.05017e-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_TEST
  Normal end of execution.

15 July 2013 09:22:28 PM