October 18 2009  11:03:02.473 AM
 
EISPACK_PRB1
  FORTRAN90 version.
 
  Sample problems for EISPACK
 
TEST01
  CG computes the eigenvalues and eigenvectors of 
  a complex general matrix.
 
  Matrix order =        4
 
  Real and imaginary parts of eigenvalues:
 
       1      4.828427      0.000000
       2      4.000000      0.000000
       3     -0.000000      0.000000
       4     -0.828427      0.000000
 
The eigenvectors are:
 
  Eigenvector        1
 
  0.653281       0.00000    
  0.500000       0.00000    
 -0.500000       0.00000    
  0.270598       0.00000    
 
  Eigenvector        2
 
  0.653281       0.00000    
 -0.500000       0.00000    
  0.500000       0.00000    
  0.270598       0.00000    
 
  Eigenvector        3
 
   0.00000      0.270598    
   0.00000     -0.500000    
   0.00000     -0.500000    
   0.00000     -0.653281    
 
  Eigenvector        4
 
   0.00000     -0.270598    
   0.00000     -0.500000    
   0.00000     -0.500000    
   0.00000      0.653281    
 
TEST02
  CH computes the eigenvalues and eigenvectors of
  a complex hermitian matrix.
 
  Matrix order =        4
 
  Error flag =        0
 
 
  The eigenvalues Lambda:
 
         1   -0.82842712    
         2    0.13322676E-14
         3     4.0000000    
         4     4.8284271    
 
 
  Eigenvectors are:
 
  Eigenvector        1
 
   0.00000      0.270598    
   0.00000      0.500000    
   0.00000      0.500000    
   0.00000      0.653281    
 
  Eigenvector        2
 
   0.00000      0.270598    
   0.00000     -0.500000    
   0.00000     -0.500000    
   0.00000      0.653281    
 
  Eigenvector        3
 
  0.653281       0.00000    
 -0.500000       0.00000    
  0.500000       0.00000    
 -0.270598       0.00000    
 
  Eigenvector        4
 
 -0.653281       0.00000    
 -0.500000       0.00000    
  0.500000      -0.00000    
  0.270598      -0.00000    
 
TEST03
  MINFIT solves an overdetermined linear system
  using least squares methods.
 
  Matrix rows =        5
  Matrix columns =        2
 
  The matrix A:
 
  Col          1             2      
  Row
 
    1       1.            1.      
    2    2.05000         -1.      
    3    3.06000          1.      
    4   -1.02000          2.      
    5    4.08000         -1.      
 
  The right hand side B:
 
  Col          1      
  Row
 
    1    1.98000    
    2   0.950000    
    3    3.98000    
    4   0.920000    
    5    2.90000    
 
  MINFIT error code IERR =        0
 
  The singular values:
 
         1     5.7385075    
         2     2.7059992    
 
  The least squares solution X:
 
         1    0.96310140    
         2    0.98854334    
 
  The residual A * X - B:
 
         1   -0.28355256E-01
         2    0.35814526E-01
         3   -0.44366372E-01
         4    0.74723261E-01
         5    0.40910368E-01
 
TEST04
  RG computes the eigenvalues and eigenvectors of
  a real general matrix.
 
  Matrix order =        3
 
  The matrix A:
 
  Col          1             2             3      
  Row
 
    1      33.           16.           72.      
    2     -24.          -10.          -57.      
    3      -8.           -4.          -17.      
 
  Real and imaginary parts of eigenvalues:
 
       1       3       0
       2       1       0
       3       2       0
 
  The eigenvectors may be complex:
 
  Eigenvector        1
 
  0.800000    
 -0.600000    
 -0.200000    
 
  Eigenvector        2
 
  -25.0000    
   20.0000    
   6.66667    
 
  Eigenvector        3
 
   48.0000    
  -39.0000    
  -12.0000    
 
Residuals (A*x-Lambda*x) for eigenvalue        1
 
   0.00000    
 -0.222045E-14
  0.444089E-15
 
Residuals (A*x-Lambda*x) for eigenvalue        2
 
  0.639488E-13
  0.497380E-13
 -0.115463E-13
 
Residuals (A*x-Lambda*x) for eigenvalue        3
 
 -0.142109E-13
  0.852651E-13
  0.355271E-13
 
TEST05:
  RGG for real generalized problem.
  Find scalars LAMBDA and vectors X so that
    A*X = LAMBDA * B * X
 
  Matrix order =        4
 
  The matrix A:
 
  Col          1             2             3             4      
  Row
 
    1      -7.            7.            6.            6.      
    2     -10.            8.           10.            8.      
    3      -8.            3.           10.           11.      
    4      -4.            0.            4.           12.      
 
  The matrix B:
 
  Col          1             2             3             4      
  Row
 
    1       2.            1.            0.            0.      
    2       1.            2.            1.            0.      
    3       0.            1.            2.            1.      
    4       0.            0.            1.            2.      
 
  Real and imaginary parts of eigenvalues:
 
       1      2.000000      0.000000
       2      1.000000      0.000000
       3      4.000000      0.000000
       4      3.000000      0.000000
 
  The eigenvectors are:
 
  Eigenvector        1
 
   1.00000    
   1.00000    
  -1.00000    
   1.00000    
 
  Eigenvector        2
 
   1.00000    
  0.750000    
  -1.00000    
   1.00000    
 
  Eigenvector        3
 
  0.666667    
  0.500000    
  -1.00000    
   1.00000    
 
  Eigenvector        4
 
  0.333333    
  0.250000    
  -1.00000    
  0.500000    
 
Residuals (A*x-(Alfr+Alfi*I)*B*x) for eigenvalue        1
 
  0.199840E-14
  0.222045E-15
 -0.888178E-15
  0.666134E-15
 
Residuals (A*x-(Alfr+Alfi*I)*B*x) for eigenvalue        2
 
  0.277556E-14
  0.210942E-14
  0.333067E-15
  0.122125E-14
 
Residuals (A*x-(Alfr+Alfi*I)*B*x) for eigenvalue        3
 
 -0.488498E-14
 -0.133227E-14
   0.00000    
 -0.355271E-14
 
Residuals (A*x-(Alfr+Alfi*I)*B*x) for eigenvalue        4
 
  0.577316E-14
  0.133227E-14
  0.888178E-15
  0.222045E-14
 
TEST06
  RS computes the eigenvalues and eigenvectors
  of a real symmetric matrix.
 
  Matrix order =        4
 
  The matrix A:
 
  Col          1             2             3             4      
  Row
 
    1       5.            4.            1.            1.      
    2       4.            5.            1.            1.      
    3       1.            1.            4.            2.      
    4       1.            1.            2.            4.      
 
  The eigenvalues Lambda:
 
         1     1.0000000    
         2     2.0000000    
         3     5.0000000    
         4     10.000000    
 
  The eigenvector matrix:
 
  Col          1             2             3             4      
  Row
 
    1   0.707107     -0.971445E-16  0.316228      0.632456    
    2  -0.707107     -0.277556E-16  0.316228      0.632456    
    3       0.        0.707107     -0.632456      0.316228    
    4       0.       -0.707107     -0.632456      0.316228    
 
  The residual (A-Lambda*I)*X:
 
  Col          1             2             3             4      
  Row
 
    1       0.       -0.360822E-15 -0.888178E-15      0.      
    2       0.       -0.499600E-15      0.        0.888178E-15
    3       0.        0.888178E-15 -0.266454E-14 -0.133227E-14
    4       0.       -0.111022E-14      0.            0.      
 
TEST07
  RSB computes the eigenvalues and eigenvectors
  of a real symmetric band matrix.
 
  Matrix order =        5
 
  The 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.      
 
  The eigenvalues Lambda:
 
         1     0.0000000    
         2     0.0000000    
         3     0.0000000    
         4     0.0000000    
         5     0.0000000    
 
  The eigenvector matrix X:
 
  Col          1             2             3             4             5      
  Row
 
    1       1.       -0.266454E-14      0.       -0.971445E-16  0.316228    
    2   0.888178E-15      1.        0.707107     -0.277556E-16 -0.632456    
    3  -0.111022E-14      0.            1.        0.707107     -0.632456    
    4  -0.888178E-15  0.888178E-15      0.            1.        0.632456    
    5       0.       -0.133227E-14      0.        0.316228          1.      
 
  The residual (A-Lambda*I)*X:
 
  Col          1             2             3             4             5      
  Row
 
    1       0.            0.            0.            0.            0.      
    2       0.            0.            0.            0.            0.      
    3   0.888178E-15 -0.888178E-15      0.           -1.       -0.632456    
    4  -0.177636E-14  0.310862E-14      0.         1.68377      0.264911    
    5   0.888178E-15 -0.355271E-14      0.       -0.367544       1.36754    
 
TEST08:
  RSG for real symmetric generalized problem.
  Find scalars LAMBDA and vectors X so that
    A*X = LAMBDA * B * X
 
  Matrix order =        4
 
  The matrix A:
 
  Col          1             2             3             4      
  Row
 
    1       0.            1.            2.            3.      
    2       1.            0.            1.            2.      
    3       2.            1.            0.            1.      
    4       3.            2.            1.            0.      
 
  The matrix B:
 
  Col          1             2             3             4      
  Row
 
    1       2.           -1.            0.            0.      
    2      -1.            2.           -1.            0.      
    3       0.           -1.            2.           -1.      
    4       0.            0.           -1.            2.      
 
  The eigenvalues Lambda:
 
         1    -2.4357817    
         2   -0.52079729    
         3   -0.16421833    
         4     11.520797    
 
  The eigenvector matrix X:
 
  Col          1             2             3             4      
  Row
 
    1   0.526940      0.251292     -0.149448      0.660948    
    2   0.287038     -0.409656      0.342942      0.912240    
    3  -0.287038     -0.409656     -0.342942      0.912240    
    4  -0.526940      0.251292      0.149448      0.660948    
 
Residuals (A*x-(w*I)*B*x) for eigenvalue        1
 
 -0.222045E-15
  0.111022E-15
  0.133227E-14
 -0.133227E-14
 
Residuals (A*x-(w*I)*B*x) for eigenvalue        2
 
  0.222045E-15
 -0.721645E-15
 -0.693889E-15
  0.183187E-14
 
Residuals (A*x-(w*I)*B*x) for eigenvalue        3
 
  0.929812E-15
 -0.256739E-15
  0.534295E-15
  0.107553E-14
 
Residuals (A*x-(w*I)*B*x) for eigenvalue        4
 
  0.355271E-14
 -0.177636E-14
 -0.177636E-14
  0.355271E-14
 
TEST09:
  RSGAB for real symmetric generalized problem.
  Find scalars LAMBDA and vectors X so that
    A*B*X = LAMBDA * X
 
  Matrix order =        4
 
  The matrix A:
 
  Col          1             2             3             4      
  Row
 
    1       0.            1.            2.            3.      
    2       1.            0.            1.            2.      
    3       2.            1.            0.            1.      
    4       3.            2.            1.            0.      
 
  The matrix B:
 
  Col          1             2             3             4      
  Row
 
    1       2.           -1.            0.            0.      
    2      -1.            2.           -1.            0.      
    3       0.           -1.            2.           -1.      
    4       0.            0.           -1.            2.      
 
  EThe eigenvalues Lambda:
 
         1    -5.0000000    
         2    -2.0000000    
         3    -2.0000000    
         4     3.0000000    
 
  The eigenvector matrix X:
 
  Col          1             2             3             4      
  Row
 
    1   0.547723     -0.171729E-16  0.314018E-15  0.707107    
    2   0.182574      0.325082E-01  0.815849      0.707107    
    3  -0.182574     -0.690292      0.436078      0.707107    
    4  -0.547723     -0.138588E-15  0.644493E-16  0.707107    
 
  The residual matrix (A*B-Lambda*I)*X:
 
  Col          1             2             3             4      
  Row
 
    1   0.355271E-14  0.766765E-16  0.461504E-15 -0.444089E-15
    2   0.199840E-14 -0.222045E-15  0.222045E-15 -0.444089E-15
    3   0.122125E-14 -0.111022E-14  0.888178E-15      0.      
    4  -0.444089E-15 -0.551323E-16  0.128769E-14  0.444089E-15
 
TEST10:
  RSGBA for real symmetric generalized problem.
  Find scalars LAMBDA and vectors X so that
    B*A*X = LAMBDA * X
 
  Matrix order =        4
 
  The matrix A:
 
  Col          1             2             3             4      
  Row
 
    1       0.            1.            2.            3.      
    2       1.            0.            1.            2.      
    3       2.            1.            0.            1.      
    4       3.            2.            1.            0.      
 
  The matrix B:
 
  Col          1             2             3             4      
  Row
 
    1       2.           -1.            0.            0.      
    2      -1.            2.           -1.            0.      
    3       0.           -1.            2.           -1.      
    4       0.            0.           -1.            2.      
 
  The eigenvalues Lambda:
 
         1    -5.0000000    
         2    -2.0000000    
         3    -2.0000000    
         4     3.0000000    
 
  The eigenvector matrix X:
 
  Col          1             2             3             4      
  Row
 
    1   0.912871     -0.325082E-01 -0.815849      0.707107    
    2  -0.222045E-15  0.755308       1.19562     -0.166533E-15
    3   0.388578E-15  -1.41309      0.563058E-01 -0.277556E-16
    4  -0.912871      0.690292     -0.436078      0.707107    
 
  The residual matrix (B*A-Lambda*I)*X:
 
  Col          1             2             3             4      
  Row
 
    1   0.532907E-14 -0.735523E-15 -0.222045E-15 -0.888178E-15
    2  -0.888178E-15  0.666134E-15 -0.888178E-15  0.138778E-14
    3   0.105471E-14 -0.133227E-14  0.166533E-15 -0.360822E-15
    4  -0.266454E-14  0.444089E-15  0.222045E-15      0.      
 
TEST11
  RSM computes some eigenvalues and eigenvectors
  of a real symmetric matrix.
 
  Matrix order =        4
  Number of eigenvectors desired =        4
 
  The matrix A:
 
  Col          1             2             3             4      
  Row
 
    1       5.            4.            1.            1.      
    2       4.            5.            1.            1.      
    3       1.            1.            4.            2.      
    4       1.            1.            2.            4.      
 
  The eigenvalues Lambda:
 
         1     1.0000000    
         2     2.0000000    
         3     5.0000000    
         4     10.000000    
 
  The eigenvector matrix X:
 
  Col          1             2             3             4      
  Row
 
    1   0.707107     -0.222045E-15  0.316228      0.632456    
    2  -0.707107     -0.555112E-16  0.316228      0.632456    
    3       0.        0.707107     -0.632456      0.316228    
    4       0.       -0.707107     -0.632456      0.316228    
 
  The residual (A-Lambda*I)*X:
 
  Col          1             2             3             4      
  Row
 
    1       0.       -0.333067E-15 -0.266454E-14 -0.266454E-14
    2       0.       -0.444089E-15 -0.155431E-14 -0.266454E-14
    3       0.        0.888178E-15 -0.310862E-14  0.222045E-14
    4       0.        0.666134E-15  0.888178E-15  0.177636E-14
 
TEST12
  RSP computes the eigenvalues and eigenvectors
  of a real symmetric packed matrix.
 
  Matrix order =        4
 
  The matrix A:
 
  Col          1             2             3             4      
  Row
 
    1       5.            4.            1.            1.      
    2       4.            5.            1.            1.      
    3       1.            1.            4.            2.      
    4       1.            1.            2.            4.      
 
  The eigenvalues Lambda:
 
         1     1.0000000    
         2     2.0000000    
         3     5.0000000    
         4     10.000000    
 
  The eigenvector matrix X:
 
  Col          1             2             3             4      
  Row
 
    1   0.707107      0.555112E-16  0.316228      0.632456    
    2  -0.707107      0.111022E-15  0.316228      0.632456    
    3       0.        0.707107     -0.632456      0.316228    
    4       0.       -0.707107     -0.632456      0.316228    
 
  The residual matrix (A-Lambda*I)*X:
 
  Col          1             2             3             4      
  Row
 
    1       0.        0.777156E-15 -0.177636E-14 -0.888178E-15
    2       0.        0.777156E-15 -0.666134E-15      0.      
    3       0.        0.133227E-14 -0.222045E-14 -0.888178E-15
    4       0.       -0.222045E-15 -0.888178E-15      0.      
 
TEST13
  RSPP finds some eigenvalues and eigenvectors of
  a real symmetric packed matrix.
 
  Matrix order =        4
 
  The matrix A:
 
  Col          1             2             3             4      
  Row
 
    1       5.            4.            1.            1.      
    2       4.            5.            1.            1.      
    3       1.            1.            4.            2.      
    4       1.            1.            2.            4.      
 
  The eigenvalues Lambda:
 
         1     1.0000000    
         2     2.0000000    
         3     5.0000000    
         4     10.000000    
 
  The eigenvector matrix X:
 
  Col          1             2             3             4      
  Row
 
    1   0.707107     -0.555112E-16  0.316228     -0.632456    
    2  -0.707107      0.111022E-15  0.316228     -0.632456    
    3       0.        0.707107     -0.632456     -0.316228    
    4       0.       -0.707107     -0.632456     -0.316228    
 
  The residual matrix (A-Lambda*I)*X:
 
  Col          1             2             3             4      
  Row
 
    1       0.        0.555112E-15 -0.333067E-14  0.888178E-15
    2       0.        0.444089E-15 -0.222045E-14      0.      
    3       0.        0.133227E-14 -0.310862E-14  0.888178E-15
    4       0.            0.        0.222045E-14      0.      
 
TEST14
  RST computes the eigenvalues and eigenvectors
  of a real symmetric tridiagonal matrix.
 
  Matrix order =        5
 
  The 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.      
 
  The eigenvalues Lambda:
 
         1    0.26794919    
         2     1.0000000    
         3     2.0000000    
         4     3.0000000    
         5     3.7320508    
 
  The eigenvector matrix X:
 
  Col          1             2             3             4             5      
  Row
 
    1  -0.288675      0.500000     -0.577350     -0.500000     -0.288675    
    2  -0.500000      0.500000      0.346252E-15  0.500000      0.500000    
    3  -0.577350     -0.226647E-15  0.577350     -0.489055E-15 -0.577350    
    4  -0.500000     -0.500000     -0.150268E-15 -0.500000      0.500000    
    5  -0.288675     -0.500000     -0.577350      0.500000     -0.288675    
 
  The residual matrix (A-Lambda*I)*X:
 
  Col          1             2             3             4             5      
  Row
 
    1  -0.555112E-15      0.       -0.444089E-15 -0.222045E-15      0.      
    2       0.       -0.222045E-15 -0.359436E-15      0.            0.      
    3  -0.249800E-15 -0.509091E-16 -0.222045E-15 -0.871483E-16      0.      
    4  -0.832667E-16  0.166533E-15 -0.325319E-16      0.            0.      
    5  -0.180411E-15  0.444089E-15  0.222045E-15 -0.222045E-15  0.444089E-15
 
TEST15
  RT computes the eigenvalues and eigenvectors
  of a real sign-symmetric tridiagonal matrix.
 
  Matrix order =        5
 
  The 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.      
 
  The eigenvalues Lambda:
 
         1    0.26794919    
         2     1.0000000    
         3     2.0000000    
         4     3.0000000    
         5     3.7320508    
 
  The eigenvector matrix X:
 
  Col          1             2             3             4             5      
  Row
 
    1  -0.288675      0.500000     -0.577350     -0.500000     -0.288675    
    2  -0.500000      0.500000      0.346252E-15  0.500000      0.500000    
    3  -0.577350     -0.226647E-15  0.577350     -0.489055E-15 -0.577350    
    4  -0.500000     -0.500000     -0.150268E-15 -0.500000      0.500000    
    5  -0.288675     -0.500000     -0.577350      0.500000     -0.288675    
 
  The residual matrix (A-Lambda*I)*X:
 
  Col          1             2             3             4             5      
  Row
 
    1  -0.555112E-15      0.       -0.444089E-15 -0.222045E-15      0.      
    2       0.       -0.222045E-15 -0.359436E-15      0.            0.      
    3  -0.249800E-15 -0.509091E-16 -0.222045E-15 -0.871483E-16      0.      
    4  -0.832667E-16  0.166533E-15 -0.325319E-16      0.            0.      
    5  -0.180411E-15  0.444089E-15  0.222045E-15 -0.222045E-15  0.444089E-15
 
TEST16
  SVD computes the singular value decomposition
  of a real general matrix.
 
  Matrix order =        4
 
  The matrix A:
 
  Col          1             2             3             4      
  Row
 
    1   0.990000      0.200000E-02  0.600000E-02  0.200000E-02
    2   0.200000E-02  0.990000      0.200000E-02  0.600000E-02
    3   0.600000E-02  0.200000E-02  0.990000      0.200000E-02
    4   0.200000E-02  0.600000E-02  0.200000E-02  0.990000    
 
  The singular values S
 
         1     1.0000000    
         2    0.98400000    
         3    0.99200000    
         4    0.98400000    
 
  The U matrix:
 
  Col          1             2             3             4      
  Row
 
    1  -0.500000     -0.707107      0.500000     -0.219026E-18
    2  -0.500000      0.104916E-13 -0.500000      0.707107    
    3  -0.500000      0.707107      0.500000      0.194289E-14
    4  -0.500000      0.124623E-13 -0.500000     -0.707107    
 
  The V matrix:
 
  Col          1             2             3             4      
  Row
 
    1  -0.500000     -0.707107      0.500000         -0.      
    2  -0.500000      0.104916E-13 -0.500000      0.707107    
    3  -0.500000      0.707107      0.500000      0.194289E-14
    4  -0.500000      0.125178E-13 -0.500000     -0.707107    
 
  The product U * S * Transpose(V):
 
  Col          1             2             3             4      
  Row
 
    1   0.990000      0.200000E-02  0.600000E-02  0.200000E-02
    2   0.200000E-02  0.990000      0.200000E-02  0.600000E-02
    3   0.600000E-02  0.200000E-02  0.990000      0.200000E-02
    4   0.200000E-02  0.600000E-02  0.200000E-02  0.990000    
 
EISPACK_PRB1
  Normal end of execution.
 
October 18 2009  11:03:02.494 AM
