Operator Reference

HALCON Operator Reference / Matrix / Eigenvalues

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generalized_eigenvalues_general_matrixT_generalized_eigenvalues_general_matrixGeneralizedEigenvaluesGeneralMatrixGeneralizedEigenvaluesGeneralMatrixgeneralized_eigenvalues_general_matrix (Operator)

generalized_eigenvalues_general_matrixT_generalized_eigenvalues_general_matrixGeneralizedEigenvaluesGeneralMatrixGeneralizedEigenvaluesGeneralMatrixgeneralized_eigenvalues_general_matrix — Compute the generalized eigenvalues and optionally the generalized eigenvectors of general matrices.

Signature

generalized_eigenvalues_general_matrix( : : MatrixAID, MatrixBID, ComputeEigenvectors : EigenvaluesRealID, EigenvaluesImagID, EigenvectorsRealID, EigenvectorsImagID)

Herror T_generalized_eigenvalues_general_matrix(const Htuple MatrixAID, const Htuple MatrixBID, const Htuple ComputeEigenvectors, Htuple* EigenvaluesRealID, Htuple* EigenvaluesImagID, Htuple* EigenvectorsRealID, Htuple* EigenvectorsImagID)

void GeneralizedEigenvaluesGeneralMatrix(const HTuple& MatrixAID, const HTuple& MatrixBID, const HTuple& ComputeEigenvectors, HTuple* EigenvaluesRealID, HTuple* EigenvaluesImagID, HTuple* EigenvectorsRealID, HTuple* EigenvectorsImagID)

void HMatrix::GeneralizedEigenvaluesGeneralMatrix(const HMatrix& MatrixBID, const HString& ComputeEigenvectors, HMatrix* EigenvaluesRealID, HMatrix* EigenvaluesImagID, HMatrix* EigenvectorsRealID, HMatrix* EigenvectorsImagID) const

void HMatrix::GeneralizedEigenvaluesGeneralMatrix(const HMatrix& MatrixBID, const char* ComputeEigenvectors, HMatrix* EigenvaluesRealID, HMatrix* EigenvaluesImagID, HMatrix* EigenvectorsRealID, HMatrix* EigenvectorsImagID) const

void HMatrix::GeneralizedEigenvaluesGeneralMatrix(const HMatrix& MatrixBID, const wchar_t* ComputeEigenvectors, HMatrix* EigenvaluesRealID, HMatrix* EigenvaluesImagID, HMatrix* EigenvectorsRealID, HMatrix* EigenvectorsImagID) const   ( Windows only)

static void HOperatorSet.GeneralizedEigenvaluesGeneralMatrix(HTuple matrixAID, HTuple matrixBID, HTuple computeEigenvectors, out HTuple eigenvaluesRealID, out HTuple eigenvaluesImagID, out HTuple eigenvectorsRealID, out HTuple eigenvectorsImagID)

void HMatrix.GeneralizedEigenvaluesGeneralMatrix(HMatrix matrixBID, string computeEigenvectors, out HMatrix eigenvaluesRealID, out HMatrix eigenvaluesImagID, out HMatrix eigenvectorsRealID, out HMatrix eigenvectorsImagID)

def generalized_eigenvalues_general_matrix(matrix_aid: HHandle, matrix_bid: HHandle, compute_eigenvectors: str) -> Tuple[HHandle, HHandle, HHandle, HHandle]

Description

The operator generalized_eigenvalues_general_matrixgeneralized_eigenvalues_general_matrixGeneralizedEigenvaluesGeneralMatrixGeneralizedEigenvaluesGeneralMatrixgeneralized_eigenvalues_general_matrix computes all generalized eigenvalues and, optionally, the left or right generalized eigenvectors of the square, general matrices MatrixA and MatrixB. Both matrices must have identical dimensions. The matrices are defined by the matrix handles MatrixAIDMatrixAIDMatrixAIDmatrixAIDmatrix_aid and MatrixBIDMatrixBIDMatrixBIDmatrixBIDmatrix_bid. The computed eigenvectors have the norm 1.

The operator generates the new matrices EigenvaluesReal and EigenvaluesImag with the real and the imaginary parts of the computed eigenvalues. Each matrix has one column and n rows, where n is the number of rows or columns of the input matrices. In contrast to the operator generalized_eigenvalues_symmetric_matrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrixgeneralized_eigenvalues_symmetric_matrix, the order of the generalized eigenvalues is not defined. The operator returns the matrix handles EigenvaluesRealIDEigenvaluesRealIDEigenvaluesRealIDeigenvaluesRealIDeigenvalues_real_id and EigenvaluesImagIDEigenvaluesImagIDEigenvaluesImagIDeigenvaluesImagIDeigenvalues_imag_id. If desired, the real and imaginary parts of the respective eigenvectors are stored in the new matrices EigenvectorsReal and EigenvectorsImag. Here, the jth column of the matrices of eigenvectors contains the related eigenvector to the jth eigenvalue. For this, the operator returns additionally the matrix handles EigenvectorsRealIDEigenvectorsRealIDEigenvectorsRealIDeigenvectorsRealIDeigenvectors_real_id and EigenvectorsImagIDEigenvectorsImagIDEigenvectorsImagIDeigenvectorsImagIDeigenvectors_imag_id. Access to the elements of the matrix is possible, e.g., with the operator get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixget_full_matrix or get_sub_matrixget_sub_matrixGetSubMatrixGetSubMatrixget_sub_matrix.

The computation type of eigenvectors can be selected via the parameter ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectorscompute_eigenvectors. If ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectorscompute_eigenvectors = 'none'"none""none""none""none", no eigenvectors are computed and the operator is faster. For this, the matrix handles EigenvectorsRealIDEigenvectorsRealIDEigenvectorsRealIDeigenvectorsRealIDeigenvectors_real_id and EigenvectorsImagIDEigenvectorsImagIDEigenvectorsImagIDeigenvectorsImagIDeigenvectors_imag_id are invalid. If 'right'"right""right""right""right" is selected, the right generalized eigenvalues are computed. The formula for the calculation of the result is with representing the th (complex) eigenvalue and represents the corresponding (complex) eigenvector.

If 'left'"left""left""left""left" is selected, the left generalized eigenvalues are computed. The formula for the calculation of the result is with represents the conjugate-transposed of .

Example:

ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectorscompute_eigenvectors = 'right'"right""right""right""right"

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

MatrixAIDMatrixAIDMatrixAIDmatrixAIDmatrix_aid (input_control)  matrix → HMatrix, HTupleHHandleHTupleHtuple (handle) (IntPtr) (HHandle) (handle)

Matrix handle of the input matrix A.

MatrixBIDMatrixBIDMatrixBIDmatrixBIDmatrix_bid (input_control)  matrix → HMatrix, HTupleHHandleHTupleHtuple (handle) (IntPtr) (HHandle) (handle)

Matrix handle of the input matrix B.

ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectorscompute_eigenvectors (input_control)  string → HTuplestrHTupleHtuple (string) (string) (HString) (char*)

Computation of the eigenvectors.

Default: 'none' "none" "none" "none" "none"

List of values: 'left'"left""left""left""left", 'none'"none""none""none""none", 'right'"right""right""right""right"

EigenvaluesRealIDEigenvaluesRealIDEigenvaluesRealIDeigenvaluesRealIDeigenvalues_real_id (output_control)  matrix → HMatrix, HTupleHHandleHTupleHtuple (handle) (IntPtr) (HHandle) (handle)

Matrix handle with the real parts of the eigenvalues.

EigenvaluesImagIDEigenvaluesImagIDEigenvaluesImagIDeigenvaluesImagIDeigenvalues_imag_id (output_control)  matrix → HMatrix, HTupleHHandleHTupleHtuple (handle) (IntPtr) (HHandle) (handle)

Matrix handle with the imaginary parts of the eigenvalues.

EigenvectorsRealIDEigenvectorsRealIDEigenvectorsRealIDeigenvectorsRealIDeigenvectors_real_id (output_control)  matrix → HMatrix, HTupleHHandleHTupleHtuple (handle) (IntPtr) (HHandle) (handle)

Matrix handle with the real parts of the eigenvectors.

EigenvectorsImagIDEigenvectorsImagIDEigenvectorsImagIDeigenvectorsImagIDeigenvectors_imag_id (output_control)  matrix → HMatrix, HTupleHHandleHTupleHtuple (handle) (IntPtr) (HHandle) (handle)

Matrix handle with the imaginary parts of the eigenvectors.

Result

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

Possible Predecessors

create_matrixcreate_matrixCreateMatrixCreateMatrixcreate_matrix

Possible Successors

get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixget_full_matrix, get_value_matrixget_value_matrixGetValueMatrixGetValueMatrixget_value_matrix, get_diagonal_matrixget_diagonal_matrixGetDiagonalMatrixGetDiagonalMatrixget_diagonal_matrix

See also

generalized_eigenvalues_symmetric_matrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrixgeneralized_eigenvalues_symmetric_matrix, eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixeigenvalues_symmetric_matrix, eigenvalues_general_matrixeigenvalues_general_matrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixeigenvalues_general_matrix

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

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ClassesClasses | | Operators