26 February  2021  11:31:09.065 AM      

JACOBI_EIGENVALUE_TEST
  FORTRAN77 version
  Test JACOBI_EIGENVALUE().

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:   4.00000      -30.0000       60.0000      -35.0000    
    2:  -30.0000       300.000      -675.000       420.000    
    3:   60.0000      -675.000       1620.00      -1050.00    
    4:  -35.0000       420.000      -1050.00       700.000    

  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 =   0.120349E-11

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:   4.00000       0.00000       0.00000       0.00000    
    2:   0.00000       1.00000       0.00000       0.00000    
    3:   0.00000       0.00000       3.00000       0.00000    
    4:   0.00000       0.00000       0.00000       2.00000    

  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:   0.00000       0.00000       0.00000       1.00000    
    2:   1.00000       0.00000       0.00000       0.00000    
    3:   0.00000       0.00000       1.00000       0.00000    
    4:   0.00000       1.00000       0.00000       0.00000    

  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:  -2.00000       1.00000       0.00000       0.00000       0.00000    
    2:   1.00000      -2.00000       1.00000       0.00000       0.00000    
    3:   0.00000       1.00000      -2.00000       1.00000       0.00000    
    4:   0.00000       0.00000       1.00000      -2.00000       1.00000    
    5:   0.00000       0.00000       0.00000       1.00000      -2.00000    

  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 =   0.940195E-15

JACOBI_EIGENVALUE_TEST
  Normal end of execution.

26 February  2021  11:31:09.065 AM