GENEIG Call

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GENEIG Call

computes eigenvalues and eigenvectors of a generalized eigenproblem

CALL GENEIG( eigenvalues, eigenvectors, symmetric-matrix1,

symmetric-matrix2);

The inputs to the GENEIG subroutine are as follows:

eigenvalues: is a returned vector containing the eigenvalues.
eigenvectors: is a returned matrix containing the corresponding eigenvectors.
symmetric-matrix1: is a symmetric numeric matrix.
symmetric-matrix2: is a positive definite symmetric matrix.

The GENEIG subroutine computes eigenvalues and eigenvectors of the generalized eigenproblem. The statement

   call geneig (m,e,a,b);

computes eigenvalues M and eigenvectors E of the generalized eigenproblem A*E = B*E* diag(M), where A and B are symmetric and B is positive definite. The vector M contains the eigenvalues arranged in descending order, and the matrix E contains the corresponding eigenvectors in the columns.

The following example is from Wilkinson and Reinsch (1971, p. 311).

   a={10   2   3   1   1,
       2  12   1   2   1,
       3   1  11   1  -1,
       1   2   1   9   1,
       1   1  -1   1  15};

   b={12   1  -1   2    1,
       1  14   1  -1    1,
      -1   1  16  -1    1,
       2  -1  -1  12   -1,
       1   1   1  -1   11};

   call geneig(m,e,a,b);

The matrices produced are shown below.

              M
              1.49235
              1.10928
              0.94385
              0.66366
              0.43278

              E
             -0.07638   0.14201   0.19171  -0.08292  -0.13459
              0.01709   0.14242  -0.15899  -0.15314   0.06129
             -0.06666   0.12099   0.07483   0.11860   0.15790
              0.08604   0.12553  -0.13746   0.18281  -0.10946
              0.28943   0.00769   0.08897  -0.00356   0.04147

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