Name
generalized_eigenvalues_symmetric_matrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrix — Compute the generalized eigenvalues and optionally generalized
eigenvectors of symmetric input matrices.
The operator generalized_eigenvalues_symmetric_matrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrix
computes all generalized eigenvalues and, optionally, generalized
eigenvectors of the symmetric matrix MatrixAMatrixAMatrixAMatrixAMatrixAmatrixA and the
symmetric positive definite matrix MatrixBMatrixBMatrixBMatrixBMatrixBmatrixB. Both
matrices must have identical dimensions. The matrices are
defined by the matrix handles MatrixAIDMatrixAIDMatrixAIDMatrixAIDMatrixAIDmatrixAID and
MatrixBIDMatrixBIDMatrixBIDMatrixBIDMatrixBIDmatrixBID. On output, a new matrix EigenvaluesEigenvaluesEigenvaluesEigenvaluesEigenvalueseigenvalues
with the generalized eigenvalues in ascending order and,
optionally, a new matrix
EigenvectorsEigenvectorsEigenvectorsEigenvectorsEigenvectorseigenvectors with the generalized eigenvectors is
created. Each jth column of the matrix EigenvectorsEigenvectorsEigenvectorsEigenvectorsEigenvectorseigenvectors
contains the related eigenvector to the jth eigenvalue. The
operator returns the matrix handles EigenvaluesIDEigenvaluesIDEigenvaluesIDEigenvaluesIDEigenvaluesIDeigenvaluesID and
EigenvectorsIDEigenvectorsIDEigenvectorsIDEigenvectorsIDEigenvectorsIDeigenvectorsID of the matrices EigenvaluesEigenvaluesEigenvaluesEigenvaluesEigenvalueseigenvalues and
EigenvectorsEigenvectorsEigenvectorsEigenvectorsEigenvectorseigenvectors. Access to the elements of the matrices is
possible, e.g., with the operator get_full_matrixget_full_matrixGetFullMatrixget_full_matrixGetFullMatrixGetFullMatrix or
get_sub_matrixget_sub_matrixGetSubMatrixget_sub_matrixGetSubMatrixGetSubMatrix.
The computation of generalized eigenvectors can be selected via
ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectors = 'true'"true""true""true""true""true". The formula for
the calculation of the result is
If ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectors = 'false'"false""false""false""false""false", no generalized
eigenvectors are computed. For this, the matrix handle
EigenvectorsIDEigenvectorsIDEigenvectorsIDEigenvectorsIDEigenvectorsIDeigenvectorsID is invalid.
Example:
The upper triangular parts of the input matrices MatrixAMatrixAMatrixAMatrixAMatrixAmatrixA
and MatrixBMatrixBMatrixBMatrixBMatrixBmatrixB 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
MatrixAMatrixAMatrixAMatrixAMatrixAmatrixA or MatrixBMatrixBMatrixBMatrixBMatrixBmatrixB are not of the specified
type, an exception is raised.
- Multithreading type: reentrant (runs in parallel with non-exclusive operators).
- Multithreading scope: global (may be called from any thread).
- Processed without parallelization.
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'
"false"
"false"
"false"
"false"
"false"
List of values: 'false'"false""false""false""false""false", 'true'"true""true""true""true""true"
Matrix handle with the eigenvalues.
Matrix handle with the eigenvectors.
If the parameters are valid, the operator
generalized_eigenvalues_symmetric_matrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrix returns the value
2 (H_MSG_TRUE). If necessary, an exception is raised.
create_matrixcreate_matrixCreateMatrixcreate_matrixCreateMatrixCreateMatrix
get_full_matrixget_full_matrixGetFullMatrixget_full_matrixGetFullMatrixGetFullMatrix,
get_value_matrixget_value_matrixGetValueMatrixget_value_matrixGetValueMatrixGetValueMatrix
generalized_eigenvalues_general_matrixgeneralized_eigenvalues_general_matrixGeneralizedEigenvaluesGeneralMatrixgeneralized_eigenvalues_general_matrixGeneralizedEigenvaluesGeneralMatrixGeneralizedEigenvaluesGeneralMatrix
eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrix,
eigenvalues_general_matrixeigenvalues_general_matrixEigenvaluesGeneralMatrixeigenvalues_general_matrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrix
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