| Operators |
generalized_eigenvalues_symmetric_matrix — Compute the generalized eigenvalues and optionally generalized eigenvectors of symmetric input matrices.
generalized_eigenvalues_symmetric_matrix( : : MatrixAID, MatrixBID, ComputeEigenvectors : EigenvaluesID, EigenvectorsID)
The operator generalized_eigenvalues_symmetric_matrix computes all generalized eigenvalues and, optionally, generalized eigenvectors of the symmetric matrix MatrixA and the symmetric positive definite matrix MatrixB. Both matrices must have identical dimensions. The matrices are defined by the matrix handles MatrixAID and MatrixBID. On output, a new matrix Eigenvalues with the generalized eigenvalues in ascending order and, optionally, a new matrix Eigenvectors with the generalized eigenvectors is created. Each jth column of the matrix Eigenvectors contains the related eigenvector to the jth eigenvalue. The operator returns the matrix handles EigenvaluesID and EigenvectorsID of the matrices Eigenvalues and Eigenvectors. Access to the elements of the matrices is possible, e.g., with the operator get_full_matrix or get_sub_matrix.
The computation of generalized eigenvectors can be selected via ComputeEigenvectors = 'true'. The formula for the calculation of the result is
Example:
The upper triangular parts of the input matrices MatrixA and MatrixB must contain the relevant information of the matrices. The strictly lower triangular parts of the matrices are not referenced. If the referenced parts of the input matrices MatrixA or MatrixB are not of the specified type, an exception is raised.
Matrix handle of the symmetric input matrix A.
Matrix handle of the symmetric positive definite input matrix B.
Computation of the eigenvectors.
Default value: 'false'
List of values: 'false', 'true'
Matrix handle with the eigenvalues.
Matrix handle with the eigenvectors.
If the parameters are valid, the operator generalized_eigenvalues_symmetric_matrix returns the value 2 (H_MSG_TRUE). If necessary, an exception is raised.
get_full_matrix, get_value_matrix
generalized_eigenvalues_general_matrix
eigenvalues_symmetric_matrix, eigenvalues_general_matrix
David Poole: “Linear Algebra: A Modern Introduction”; Thomson;
Belmont; 2006.
Gene H. Golub, Charles F. van Loan: “Matrix Computations”; The
Johns Hopkins University Press; Baltimore and London; 1996.
Foundation
| Operators |