9 September 2021   5:38:53.967 PM

JACOBI_EIGENVALUE_TEST
  FORTRAN90 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          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:   0.16664286    
         2:    1.4780548    
         3:    37.101491    
         4:    2585.2538    
 
  Eigenvector matrix V:
 
  Col          1             2             3             4      
  Row
 
    1:  0.792608      0.582076      0.179186      0.291933E-01
    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 =   0.988893E-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          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:    1.0000000    
         2:    2.0000000    
         3:    3.0000000    
         4:    4.0000000    
 
  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 =    0.00000    

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          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:   -3.7320508    
         2:   -3.0000000    
         3:   -2.0000000    
         4:   -1.0000000    
         5:  -0.26794919    
 
  Eigenvector matrix V:
 
  Col          1             2             3             4             5      
  Row
 
    1:  0.288675      0.500000      0.577350     -0.500000      0.288675    
    2: -0.500000     -0.500000     -0.444985E-16 -0.500000      0.500000    
    3:  0.577350      0.505017E-16 -0.577350     -0.705760E-16  0.577350    
    4: -0.500000      0.500000      0.186451E-15  0.500000      0.500000    
    5:  0.288675     -0.500000      0.577350      0.500000      0.288675    

  Frobenius norm error in eigensystem A*V-D*V =   0.103615E-14

JACOBI_EIGENVALUE_TEST
  Normal end of execution.

 9 September 2021   5:38:53.968 PM