Language Reference
CALL GENEIG (eval, evecs, sym-matrix1, sym-matrix2);
The GENEIG subroutine computes eigenvalues and eigenvectors of a generalized eigenproblem.
The input arguments to the GENEIG subroutine are as follows:
- sym-matrix1
-
is a symmetric numeric matrix.
- sym-matrix2
-
is a positive definite symmetric matrix.
The subroutine returns the following output arguments:
- evals
-
names a vector in which the eigenvalues are returned.
- evecs
-
names a matrix in which the corresponding eigenvectors are returned.
The GENEIG subroutine computes eigenvalues and eigenvectors of the generalized eigenproblem. If 
and 
are symmetric and is positive definite, then the vector 
and the matrix 
solve the generalized eigenproblem provided that
![\[ \mb{A}*\mb{E} = \mb{B}*\mb{E}*\mbox{diag}(\mb{M}) \]](images/imlug_langref0396.png){kind=small}
The vector contains the eigenvalues arranged in descending order, and the matrix contains the corresponding eigenvectors in the columns.
The following example is from Wilkinson and Reinsch (1971):
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);
print M, E;