ClassesClassesClassesClasses | | | | Operators

eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrix (Operator)

Name

eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrix — Compute the eigenvalues and optionally eigenvectors of a symmetric matrix.

Signature

eigenvalues_symmetric_matrix( : : MatrixID, ComputeEigenvectors : EigenvaluesID, EigenvectorsID)

Herror eigenvalues_symmetric_matrix(const Hlong MatrixID, const char* ComputeEigenvectors, Hlong* EigenvaluesID, Hlong* EigenvectorsID)

Herror T_eigenvalues_symmetric_matrix(const Htuple MatrixID, const Htuple ComputeEigenvectors, Htuple* EigenvaluesID, Htuple* EigenvectorsID)

Herror eigenvalues_symmetric_matrix(const HTuple& MatrixID, const HTuple& ComputeEigenvectors, Hlong* EigenvaluesID, Hlong* EigenvectorsID)

HMatrix HMatrix::EigenvaluesSymmetricMatrix(const HTuple& ComputeEigenvectors, HMatrix* EigenvectorsID) const

void EigenvaluesSymmetricMatrix(const HTuple& MatrixID, const HTuple& ComputeEigenvectors, HTuple* EigenvaluesID, HTuple* EigenvectorsID)

HMatrix HMatrix::EigenvaluesSymmetricMatrix(const HString& ComputeEigenvectors, HMatrix* EigenvectorsID) const

HMatrix HMatrix::EigenvaluesSymmetricMatrix(const char* ComputeEigenvectors, HMatrix* EigenvectorsID) const

void HOperatorSetX.EigenvaluesSymmetricMatrix(
[in] VARIANT MatrixID, [in] VARIANT ComputeEigenvectors, [out] VARIANT* EigenvaluesID, [out] VARIANT* EigenvectorsID)

IHMatrixX* HMatrixX.EigenvaluesSymmetricMatrix(
[in] BSTR ComputeEigenvectors, [out] IHMatrixX*EigenvectorsID)

static void HOperatorSet.EigenvaluesSymmetricMatrix(HTuple matrixID, HTuple computeEigenvectors, out HTuple eigenvaluesID, out HTuple eigenvectorsID)

HMatrix HMatrix.EigenvaluesSymmetricMatrix(string computeEigenvectors, out HMatrix eigenvectorsID)

Description

The operator eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrix computes all eigenvalues and, optionally, eigenvectors of the symmetric MatrixMatrixMatrixMatrixMatrixmatrix. The matrix is defined by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDMatrixIDmatrixID. On output, a new matrix EigenvaluesEigenvaluesEigenvaluesEigenvaluesEigenvalueseigenvalues with the eigenvalues in ascending order and, optionally, a new matrix EigenvectorsEigenvectorsEigenvectorsEigenvectorsEigenvectorseigenvectors with the eigenvectors is created. 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.

The computation of eigenvectors can be selected via ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectors = 'true'"true""true""true""true""true" or ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectors = 'false'"false""false""false""false""false".

Example:


           /  6.0  5.0  3.0  \
  Matrix = |  5.0  7.0  3.0  |     ComputeEigenvectors = 'true'
           \  3.0  3.0  4.0  /

                     /  1.4195 \
  ->   Eigenvalues = |  2.1507 |
                     \ 13.4298 /

                      /  0.7842   0.0626   0.6174  \
       Eigenvectors = | -0.5667   0.4776   0.6714  |
                      \ -0.2529  -0.8763   0.4100  /

Attention

The upper triangular part of the input MatrixMatrixMatrixMatrixMatrixmatrix must contain the relevant information of the matrix. The strictly lower triangular part of the matrix is not referenced. If the referenced part of the input MatrixMatrixMatrixMatrixMatrixmatrix is not of the specified type, an exception is raised.

Parallelization

Parameters

MatrixIDMatrixIDMatrixIDMatrixIDMatrixIDmatrixID (input_control)  matrix HMatrix, HTupleHTupleHMatrix, HTupleHMatrixX, VARIANTHtuple (integer) (IntPtr) (Hlong) (Hlong) (Hlong) (Hlong)

Matrix handle of the input matrix.

ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectors (input_control)  string HTupleHTupleHTupleVARIANTHtuple (string) (string) (HString) (char*) (BSTR) (char*)

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"

EigenvaluesIDEigenvaluesIDEigenvaluesIDEigenvaluesIDEigenvaluesIDeigenvaluesID (output_control)  matrix HMatrix, HTupleHTupleHMatrix, HTupleHMatrixX, VARIANTHtuple (integer) (IntPtr) (Hlong) (Hlong) (Hlong) (Hlong)

Matrix handle with the eigenvalues.

EigenvectorsIDEigenvectorsIDEigenvectorsIDEigenvectorsIDEigenvectorsIDeigenvectorsID (output_control)  matrix HMatrix, HTupleHTupleHMatrix, HTupleHMatrixX, VARIANTHtuple (integer) (IntPtr) (Hlong) (Hlong) (Hlong) (Hlong)

Matrix handle with the eigenvectors.

Result

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

Possible Predecessors

create_matrixcreate_matrixCreateMatrixcreate_matrixCreateMatrixCreateMatrix

Possible Successors

get_full_matrixget_full_matrixGetFullMatrixget_full_matrixGetFullMatrixGetFullMatrix, get_value_matrixget_value_matrixGetValueMatrixget_value_matrixGetValueMatrixGetValueMatrix

Alternatives

eigenvalues_general_matrixeigenvalues_general_matrixEigenvaluesGeneralMatrixeigenvalues_general_matrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrix

See also

generalized_eigenvalues_symmetric_matrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrix, generalized_eigenvalues_general_matrixgeneralized_eigenvalues_general_matrixGeneralizedEigenvaluesGeneralMatrixgeneralized_eigenvalues_general_matrixGeneralizedEigenvaluesGeneralMatrixGeneralizedEigenvaluesGeneralMatrix

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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