generalized_eigenvalues_symmetric_matrixT_generalized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrix (Operator)

Name

generalized_eigenvalues_symmetric_matrixT_generalized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrix — Compute the generalized eigenvalues and optionally generalized eigenvectors of symmetric input matrices.

Signature

Description

The operator generalized_eigenvalues_symmetric_matrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrix computes all generalized eigenvalues and, optionally, generalized eigenvectors of the symmetric matrix MatrixAMatrixAMatrixAMatrixAmatrixA and the symmetric positive definite matrix MatrixBMatrixBMatrixBMatrixBmatrixB. Both matrices must have identical dimensions. The matrices are defined by the matrix handles MatrixAIDMatrixAIDMatrixAIDMatrixAIDmatrixAID and MatrixBIDMatrixBIDMatrixBIDMatrixBIDmatrixBID. On output, a new matrix EigenvaluesEigenvaluesEigenvaluesEigenvalueseigenvalues with the generalized eigenvalues in ascending order and, optionally, a new matrix EigenvectorsEigenvectorsEigenvectorsEigenvectorseigenvectors with the generalized eigenvectors is created. Each jth column of the matrix EigenvectorsEigenvectorsEigenvectorsEigenvectorseigenvectors contains the related eigenvector to the jth eigenvalue. The operator returns the matrix handles EigenvaluesIDEigenvaluesIDEigenvaluesIDEigenvaluesIDeigenvaluesID and EigenvectorsIDEigenvectorsIDEigenvectorsIDEigenvectorsIDeigenvectorsID of the matrices EigenvaluesEigenvaluesEigenvaluesEigenvalueseigenvalues and EigenvectorsEigenvectorsEigenvectorsEigenvectorseigenvectors. Access to the elements of the matrices is possible, e.g., with the operator get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrix or get_sub_matrixget_sub_matrixGetSubMatrixGetSubMatrixGetSubMatrix.

The computation of generalized eigenvectors can be selected via ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectors = 'true'"true""true""true""true". The formula for the calculation of the result is with representing the th eigenvalue and represents the corresponding eigenvector.

If ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectors = 'false'"false""false""false""false", no generalized eigenvectors are computed. For this, the matrix handle EigenvectorsIDEigenvectorsIDEigenvectorsIDEigenvectorsIDeigenvectorsID is invalid.

Example:

Attention

The upper triangular parts of the input matrices MatrixAMatrixAMatrixAMatrixAmatrixA and MatrixBMatrixBMatrixBMatrixBmatrixB 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 MatrixAMatrixAMatrixAMatrixAmatrixA or MatrixBMatrixBMatrixBMatrixBmatrixB are not of the specified type, an exception is raised.

Execution Information

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Multithreading scope: global (may be called from any thread).
• Processed without parallelization.

Parameters

Result

If the parameters are valid, the operator generalized_eigenvalues_symmetric_matrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrix returns the value 2 (H_MSG_TRUE). If necessary, an exception is raised.

Possible Predecessors

create_matrixcreate_matrixCreateMatrixCreateMatrixCreateMatrix

Possible Successors

get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrix, get_value_matrixget_value_matrixGetValueMatrixGetValueMatrixGetValueMatrix

Alternatives

generalized_eigenvalues_general_matrixgeneralized_eigenvalues_general_matrixGeneralizedEigenvaluesGeneralMatrixGeneralizedEigenvaluesGeneralMatrixGeneralizedEigenvaluesGeneralMatrix

See also

eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrix, eigenvalues_general_matrixeigenvalues_general_matrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrix

References

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.

Module

Foundation