17 January 2017 11:22:18 AM

JACOBI_EIGENVALUE_PRB
  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:        4.000000      -30.000000       60.000000      -35.000000
    1:      -30.000000      300.000000     -675.000000      420.000000
    2:       60.000000     -675.000000     1620.000000    -1050.000000
    3:      -35.000000      420.000000    -1050.000000      700.000000

  Number of iterations = 11
  Number of rotations  = 21

  Eigenvalues D:

         0:       0.166643
         1:       1.478055
         2:      37.101491
         3:    2585.253811

  Eigenvector matrix V:

  Col:          0             1             2             3     
  Row

    0:        0.792608        0.582076        0.179186        0.029193
    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

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:        4.000000        0.000000        0.000000        0.000000
    1:        0.000000        1.000000        0.000000        0.000000
    2:        0.000000        0.000000        3.000000        0.000000
    3:        0.000000        0.000000        0.000000        2.000000

  Number of iterations = 1
  Number of rotations  = 0

  Eigenvalues D:

         0:       1.000000
         1:       2.000000
         2:       3.000000
         3:       4.000000

  Eigenvector matrix V:

  Col:          0             1             2             3     
  Row

    0:        0.000000        0.000000        0.000000        1.000000
    1:        1.000000        0.000000        0.000000        0.000000
    2:        0.000000        0.000000        1.000000        0.000000
    3:        0.000000        1.000000        0.000000        0.000000

  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:       -2.000000        1.000000        0.000000        0.000000        0.000000
    1:        1.000000       -2.000000        1.000000        0.000000        0.000000
    2:        0.000000        1.000000       -2.000000        1.000000        0.000000
    3:        0.000000        0.000000        1.000000       -2.000000        1.000000
    4:        0.000000        0.000000        0.000000        1.000000       -2.000000

  Number of iterations = 10
  Number of rotations  = 43

  Eigenvalues D:

         0:      -3.732051
         1:      -3.000000
         2:      -2.000000
         3:      -1.000000
         4:      -0.267949

  Eigenvector matrix V:

  Col:          0             1             2             3             4     
  Row

    0:        0.288675        0.500000        0.577350       -0.500000        0.288675
    1:       -0.500000       -0.500000       -0.000000       -0.500000        0.500000
    2:        0.577350        0.000000       -0.577350       -0.000000        0.577350
    3:       -0.500000        0.500000        0.000000        0.500000        0.500000
    4:        0.288675       -0.500000        0.577350        0.500000        0.288675

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

JACOBI_EIGENVALUE_PRB
  Normal end of execution.

17 January 2017 11:22:18 AM